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GYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.hu HOMEPAGE OF GABOR KUN Gabor Kun Email: lastname.firstname@renyi.mta.hu Address: MTA Alfred Renyi Institute of Mathematics Realtanoda utca 13-15. Budapest, Hungary, H-1053 CV Recent publications Gabor Kun: "On sofic approximations of Property (T) groups", arxiv Gabor Kun: "Expanders admit a Lipschitz subgraph with large girth", submitted, arxiv Gabor Kun and Daniel Dadush: "Lattice sparsifiers and the approximateINTRODUCTION
LANDAU’S PROBLEMS ON PRIMES 3 where C0 is the so-called twin prime constant, (2.6) C0 = Y p>2 µ 1− 1 (p−1)2 = 0.66016 . Here and later p (as further on p HOME PAGE OF MIKLÓS RÁSONYI Miklós Rásonyi . Alfréd Rényi Institute of Mathematics Reáltanoda utca 13-15. Budapest 1053, Hungary. E-mail: mysurname.mygivenname@renyi.huISTVAN_MIKLOS
Then I changed to flute and started playing in different groups, for example, here. Recently, I'm playing again the bass in a local alternative rock band: YouTube. Kódolatlan Álmok. 128 subscribers. Subscribe. Kódolatlan Álomok - Álompár (Live @ Szimplakert, 2020.03.06) Info. Shopping. THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS 1 THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS PAUL ERD&, A. w. GOODMAN, AND LOUIS P&A 1. Introduction. Geometrically, a graph is a collection of points (or ON DECOMPOSITION OF GRAPHS ON DECOMPOSITION OF GRAPHS If a is regular, then aó = aby G. C. H. and the statement follows from Theorems 1 and 2 for finite and infinite a respectively. If a is singular thena::-S+, hence there is a regular a' satisfying max (y, b+) --a' < a. ON SOME PROBLEMS OF A STATISTICAL GROUP-THEORY. I Z. Wahrscheinlichkeitstheorie verw. Geb. 4, 175-186 (1965) On Some Problems of a Statistical Group-Theory. I BY P. ERDBS and P. TURIN 1. By statistical group-theoryMIKLÓS SIMONOVITS
Further Items; Obituaries on Paul Erdős (1913-1996) from the homepage of Peter Komjath Peter Paul Erdös and his mathematics. Papers from the International Conference held in memory of Paul Erdös in Budapest, July 4--11, 1999. THE HISTORY OF DEGENERATE (BIPARTITE) EXTREMAL GRAPH PROBLEMS Fu¨redi-Simonovits (FureSimSurvC) May15,2013 1 1. Introduction This survey describes the theory of Degenerate Extremal Graph Problems, themain results of the
GYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.hu HOMEPAGE OF GABOR KUN Gabor Kun Email: lastname.firstname@renyi.mta.hu Address: MTA Alfred Renyi Institute of Mathematics Realtanoda utca 13-15. Budapest, Hungary, H-1053 CV Recent publications Gabor Kun: "On sofic approximations of Property (T) groups", arxiv Gabor Kun: "Expanders admit a Lipschitz subgraph with large girth", submitted, arxiv Gabor Kun and Daniel Dadush: "Lattice sparsifiers and the approximateINTRODUCTION
LANDAU’S PROBLEMS ON PRIMES 3 where C0 is the so-called twin prime constant, (2.6) C0 = Y p>2 µ 1− 1 (p−1)2 = 0.66016 . Here and later p (as further on p HOME PAGE OF MIKLÓS RÁSONYI Miklós Rásonyi . Alfréd Rényi Institute of Mathematics Reáltanoda utca 13-15. Budapest 1053, Hungary. E-mail: mysurname.mygivenname@renyi.huISTVAN_MIKLOS
Then I changed to flute and started playing in different groups, for example, here. Recently, I'm playing again the bass in a local alternative rock band: YouTube. Kódolatlan Álmok. 128 subscribers. Subscribe. Kódolatlan Álomok - Álompár (Live @ Szimplakert, 2020.03.06) Info. Shopping. THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS 1 THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS PAUL ERD&, A. w. GOODMAN, AND LOUIS P&A 1. Introduction. Geometrically, a graph is a collection of points (or ON DECOMPOSITION OF GRAPHS ON DECOMPOSITION OF GRAPHS If a is regular, then aó = aby G. C. H. and the statement follows from Theorems 1 and 2 for finite and infinite a respectively. If a is singular thena::-S+, hence there is a regular a' satisfying max (y, b+) --a' < a. ON SOME PROBLEMS OF A STATISTICAL GROUP-THEORY. I Z. Wahrscheinlichkeitstheorie verw. Geb. 4, 175-186 (1965) On Some Problems of a Statistical Group-Theory. I BY P. ERDBS and P. TURIN 1. By statistical group-theoryMIKLÓS SIMONOVITS
Further Items; Obituaries on Paul Erdős (1913-1996) from the homepage of Peter Komjath Peter Paul Erdös and his mathematics. Papers from the International Conference held in memory of Paul Erdös in Budapest, July 4--11, 1999. THE HISTORY OF DEGENERATE (BIPARTITE) EXTREMAL GRAPH PROBLEMS Fu¨redi-Simonovits (FureSimSurvC) May15,2013 1 1. Introduction This survey describes the theory of Degenerate Extremal Graph Problems, themain results of the
HOMEPAGE OF MIKLÓS ABÉRT Miklós Abért. miklos.abert at renyi.mta.hu. MTA Alfréd Rényi Institute of Mathematics. Reáltanoda utca 13-15. H-1053 Budapest, Hungary. Research interest. I am interested in measured and asymptotic group theory, in particular spectral theory of graphs and groups, local sampling convergence, graph polynomials, stochastic processes ongroups
HOME PAGE OF MIKLÓS RÁSONYI Miklós Rásonyi . Alfréd Rényi Institute of Mathematics Reáltanoda utca 13-15. Budapest 1053, Hungary. E-mail: mysurname.mygivenname@renyi.huISTVAN_MIKLOS
Then I changed to flute and started playing in different groups, for example, here. Recently, I'm playing again the bass in a local alternative rock band: YouTube. Kódolatlan Álmok. 128 subscribers. Subscribe. Kódolatlan Álomok - Álompár (Live @ Szimplakert, 2020.03.06) Info. Shopping. PROBLEMS AND RESULTS ON THE THEORY OF INTERPOLATION. I PROBLEMS AND RESULTS ON THE THEORY OF INTERPOLATION. I 383 By more complicated arguments we could prove the following stronger THEOREM 2. Let n > no(A, c, #, 8) be sufficiently large, -1 - x, < x2 < HOMEPAGE OF BALÁZS SZEGEDY Balázs Szegedy. Reáltanoda utca 13-15. My main research areas are combinatorics and group theory. At the moment, I am working in various topics related to limits of discrete structures. This field is connected to combinatorics, ergodic theory and probability theory. Higher order Fourier analysis: a theory of higher order structures incompact
DISTINCT DISTANCES BETWEEN LATTICE POINTS 122 I'. ERDÖSand R. K. Guy: Distinct Distances between Lattice Points (c) it is not equidistant from any pair of the first k points . We may choose such a point provided that all n2 points are not excluded by these conditions. Condition (a) excludes at most k k\ n`^/i°gl°gn points, since there are k\ circles \2/ 2, round each of k points, and each circle contains at most n /1 °g °g'n THE SUBCONVEXITY PROBLEM FOR RANKIN SELBERG L-FUNCTIONS. II 4 G. HARCOS AND P. MICHEL This result states the equidistribution of orbits of Heegner points by subgroups Gof G K of index satisfying = o(D 1 23042); this is a special instance of equidistribution for short orbits of Heegner points on Shimura curves associated to inde nite quaternion algebras2 over Q and is meaningful in the context of the Andr e{Oort conjectures. ON THE ASYMPTOTIC BEHAVIOR OF LARGE PRIME FACTORS OF … pacific journal 0~ mathematics vol. 82, no. 2, 1979 on the asymptotic behavior of large prime factors of integers k. alladi and p. erd& UNSOLVED PROBLEMS HEPA3PELHEHHB1E FIPO&IEMBI 222 ERDÖS LANDAU. HARDY and LITTLEWOOD proved by BRUN'S method that A conjecture weaker than (I. 1.1) but stronger than (I. 1.3) would be: To every E > 0 there exists a yo so that for y > yo (I. 1.4) 70 + y) -n(x) < (1 + E) y log y* The replacement in (I. 1.3) of 2 by a smaller constant would be of greatLÁSZLÓ CSIRMAZ
László Csirmaz. I do research in Set Theory, Combinatorics, and Mathematical Logic. My favourite subject, however, is Cryptography, especially secret sharing. You can write to me at . This stellar icosi-dodecahedron had been in the CEU Computer Lab . I made it from green cardboard paper. HOMEPAGE OF GABOR KUN Gabor Kun Email: lastname.firstname@renyi.mta.hu Address: MTA Alfred Renyi Institute of Mathematics Realtanoda utca 13-15. Budapest, Hungary, H-1053 CV Recent publications Gabor Kun: "On sofic approximations of Property (T) groups", arxiv Gabor Kun: "Expanders admit a Lipschitz subgraph with large girth", submitted, arxiv Gabor Kun and Daniel Dadush: "Lattice sparsifiers and the approximateGYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.huINTRODUCTION
LANDAU’S PROBLEMS ON PRIMES 3 where C0 is the so-called twin prime constant, (2.6) C0 = Y p>2 µ 1− 1 (p−1)2 = 0.66016 . Here and later p (as further on p HOME PAGE OF MIKLÓS RÁSONYI Miklós Rásonyi . Alfréd Rényi Institute of Mathematics Reáltanoda utca 13-15. Budapest 1053, Hungary. E-mail: mysurname.mygivenname@renyi.hu THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS 1 THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS PAUL ERD&, A. w. GOODMAN, AND LOUIS P&A 1. Introduction. Geometrically, a graph is a collection of points (or ON DECOMPOSITION OF GRAPHS ON DECOMPOSITION OF GRAPHS If a is regular, then aó = aby G. C. H. and the statement follows from Theorems 1 and 2 for finite and infinite a respectively. If a is singular thena::-S+, hence there is a regular a' satisfying max (y, b+) --a' < a. ON SOME PROBLEMS OF A STATISTICAL GROUP-THEORY. I Z. Wahrscheinlichkeitstheorie verw. Geb. 4, 175-186 (1965) On Some Problems of a Statistical Group-Theory. I BY P. ERDBS and P. TURIN 1. By statistical group-theory SOME PROBLEMS AND RESULTS ON THE IRRATIONALITY OF … 2 IRRATIONALITY OF THE SUM OF INFINITE SERIES lim supnk'rk = oo• (4) k=m Then a is a Liouville number. It is easy to see that Theorem 1 is best possible. It is well known and easy to see that for every A there is a sequence nk satisfying nk > A2k for every k > 0 but i I isrational.
THE HISTORY OF DEGENERATE (BIPARTITE) EXTREMAL GRAPH PROBLEMS Fu¨redi-Simonovits (FureSimSurvC) May15,2013 1 1. Introduction This survey describes the theory of Degenerate Extremal Graph Problems, themain results of the
MIKLÓS SIMONOVITS
Further Items; Obituaries on Paul Erdős (1913-1996) from the homepage of Peter Komjath Peter Paul Erdös and his mathematics. Papers from the International Conference held in memory of Paul Erdös in Budapest, July 4--11, 1999. HOMEPAGE OF GABOR KUN Gabor Kun Email: lastname.firstname@renyi.mta.hu Address: MTA Alfred Renyi Institute of Mathematics Realtanoda utca 13-15. Budapest, Hungary, H-1053 CV Recent publications Gabor Kun: "On sofic approximations of Property (T) groups", arxiv Gabor Kun: "Expanders admit a Lipschitz subgraph with large girth", submitted, arxiv Gabor Kun and Daniel Dadush: "Lattice sparsifiers and the approximateGYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.huINTRODUCTION
LANDAU’S PROBLEMS ON PRIMES 3 where C0 is the so-called twin prime constant, (2.6) C0 = Y p>2 µ 1− 1 (p−1)2 = 0.66016 . Here and later p (as further on p HOME PAGE OF MIKLÓS RÁSONYI Miklós Rásonyi . Alfréd Rényi Institute of Mathematics Reáltanoda utca 13-15. Budapest 1053, Hungary. E-mail: mysurname.mygivenname@renyi.hu THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS 1 THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS PAUL ERD&, A. w. GOODMAN, AND LOUIS P&A 1. Introduction. Geometrically, a graph is a collection of points (or ON DECOMPOSITION OF GRAPHS ON DECOMPOSITION OF GRAPHS If a is regular, then aó = aby G. C. H. and the statement follows from Theorems 1 and 2 for finite and infinite a respectively. If a is singular thena::-S+, hence there is a regular a' satisfying max (y, b+) --a' < a. ON SOME PROBLEMS OF A STATISTICAL GROUP-THEORY. I Z. Wahrscheinlichkeitstheorie verw. Geb. 4, 175-186 (1965) On Some Problems of a Statistical Group-Theory. I BY P. ERDBS and P. TURIN 1. By statistical group-theory SOME PROBLEMS AND RESULTS ON THE IRRATIONALITY OF … 2 IRRATIONALITY OF THE SUM OF INFINITE SERIES lim supnk'rk = oo• (4) k=m Then a is a Liouville number. It is easy to see that Theorem 1 is best possible. It is well known and easy to see that for every A there is a sequence nk satisfying nk > A2k for every k > 0 but i I isrational.
THE HISTORY OF DEGENERATE (BIPARTITE) EXTREMAL GRAPH PROBLEMS Fu¨redi-Simonovits (FureSimSurvC) May15,2013 1 1. Introduction This survey describes the theory of Degenerate Extremal Graph Problems, themain results of the
MIKLÓS SIMONOVITS
Further Items; Obituaries on Paul Erdős (1913-1996) from the homepage of Peter Komjath Peter Paul Erdös and his mathematics. Papers from the International Conference held in memory of Paul Erdös in Budapest, July 4--11, 1999.GYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.hu HOMEPAGE OF MIKLÓS ABÉRT Miklós Abért. miklos.abert at renyi.mta.hu. MTA Alfréd Rényi Institute of Mathematics. Reáltanoda utca 13-15. H-1053 Budapest, Hungary. Research interest. I am interested in measured and asymptotic group theory, in particular spectral theory of graphs and groups, local sampling convergence, graph polynomials, stochastic processes ongroups
HOME PAGE OF MIKLÓS RÁSONYI Miklós Rásonyi . Alfréd Rényi Institute of Mathematics Reáltanoda utca 13-15. Budapest 1053, Hungary. E-mail: mysurname.mygivenname@renyi.huISTVAN_MIKLOS
Then I changed to flute and started playing in different groups, for example, here. Recently, I'm playing again the bass in a local alternative rock band: YouTube. Kódolatlan Álmok. 128 subscribers. Subscribe. Kódolatlan Álomok - Álompár (Live @ Szimplakert, 2020.03.06) Info. Shopping. PROBLEMS AND RESULTS ON THE THEORY OF INTERPOLATION. I PROBLEMS AND RESULTS ON THE THEORY OF INTERPOLATION. I 383 By more complicated arguments we could prove the following stronger THEOREM 2. Let n > no(A, c, #, 8) be sufficiently large, -1 - x, < x2 < HOMEPAGE OF BALÁZS SZEGEDY Balázs Szegedy. Reáltanoda utca 13-15. My main research areas are combinatorics and group theory. At the moment, I am working in various topics related to limits of discrete structures. This field is connected to combinatorics, ergodic theory and probability theory. Higher order Fourier analysis: a theory of higher order structures incompact
DISTINCT DISTANCES BETWEEN LATTICE POINTS 122 I'. ERDÖSand R. K. Guy: Distinct Distances between Lattice Points (c) it is not equidistant from any pair of the first k points . We may choose such a point provided that all n2 points are not excluded by these conditions. Condition (a) excludes at most k k\ n`^/i°gl°gn points, since there are k\ circles \2/ 2, round each of k points, and each circle contains at most n /1 °g °g'n UNSOLVED PROBLEMS HEPA3PELHEHHB1E FIPO&IEMBI 222 ERDÖS LANDAU. HARDY and LITTLEWOOD proved by BRUN'S method that A conjecture weaker than (I. 1.1) but stronger than (I. 1.3) would be: To every E > 0 there exists a yo so that for y > yo (I. 1.4) 70 + y) -n(x) < (1 + E) y log y* The replacement in (I. 1.3) of 2 by a smaller constant would be of great ON THE ASYMPTOTIC BEHAVIOR OF LARGE PRIME FACTORS OF … pacific journal 0~ mathematics vol. 82, no. 2, 1979 on the asymptotic behavior of large prime factors of integers k. alladi and p. erd&LÁSZLÓ CSIRMAZ
László Csirmaz. I do research in Set Theory, Combinatorics, and Mathematical Logic. My favourite subject, however, is Cryptography, especially secret sharing. You can write to me at . This stellar icosi-dodecahedron had been in the CEU Computer Lab . I made it from green cardboard paper. HOMEPAGE OF GABOR KUN Gabor Kun Email: lastname.firstname@renyi.mta.hu Address: MTA Alfred Renyi Institute of Mathematics Realtanoda utca 13-15. Budapest, Hungary, H-1053 CV Recent publications Gabor Kun: "On sofic approximations of Property (T) groups", arxiv Gabor Kun: "Expanders admit a Lipschitz subgraph with large girth", submitted, arxiv Gabor Kun and Daniel Dadush: "Lattice sparsifiers and the approximateGYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.huINTRODUCTION
LANDAU’S PROBLEMS ON PRIMES 3 where C0 is the so-called twin prime constant, (2.6) C0 = Y p>2 µ 1− 1 (p−1)2 = 0.66016 . Here and later p (as further on p HOME PAGE OF MIKLÓS RÁSONYI Miklós Rásonyi . Alfréd Rényi Institute of Mathematics Reáltanoda utca 13-15. Budapest 1053, Hungary. E-mail: mysurname.mygivenname@renyi.hu ON SOME PROBLEMS OF A STATISTICAL GROUP-THEORY. I Z. Wahrscheinlichkeitstheorie verw. Geb. 4, 175-186 (1965) On Some Problems of a Statistical Group-Theory. I BY P. ERDBS and P. TURIN 1. By statistical group-theory THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS 1 THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS PAUL ERD&, A. w. GOODMAN, AND LOUIS P&A 1. Introduction. Geometrically, a graph is a collection of points (or ON DECOMPOSITION OF GRAPHS ON DECOMPOSITION OF GRAPHS If a is regular, then aó = aby G. C. H. and the statement follows from Theorems 1 and 2 for finite and infinite a respectively. If a is singular thena::-S+, hence there is a regular a' satisfying max (y, b+) --a' < a. SOME PROBLEMS AND RESULTS ON THE IRRATIONALITY OF … 2 IRRATIONALITY OF THE SUM OF INFINITE SERIES lim supnk'rk = oo• (4) k=m Then a is a Liouville number. It is easy to see that Theorem 1 is best possible. It is well known and easy to see that for every A there is a sequence nk satisfying nk > A2k for every k > 0 but i I isrational.
THE HISTORY OF DEGENERATE (BIPARTITE) EXTREMAL GRAPH PROBLEMS Fu¨redi-Simonovits (FureSimSurvC) May15,2013 1 1. Introduction This survey describes the theory of Degenerate Extremal Graph Problems, themain results of the
MIKLÓS SIMONOVITS
Further Items; Obituaries on Paul Erdős (1913-1996) from the homepage of Peter Komjath Peter Paul Erdös and his mathematics. Papers from the International Conference held in memory of Paul Erdös in Budapest, July 4--11, 1999. HOMEPAGE OF GABOR KUN Gabor Kun Email: lastname.firstname@renyi.mta.hu Address: MTA Alfred Renyi Institute of Mathematics Realtanoda utca 13-15. Budapest, Hungary, H-1053 CV Recent publications Gabor Kun: "On sofic approximations of Property (T) groups", arxiv Gabor Kun: "Expanders admit a Lipschitz subgraph with large girth", submitted, arxiv Gabor Kun and Daniel Dadush: "Lattice sparsifiers and the approximateGYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.huINTRODUCTION
LANDAU’S PROBLEMS ON PRIMES 3 where C0 is the so-called twin prime constant, (2.6) C0 = Y p>2 µ 1− 1 (p−1)2 = 0.66016 . Here and later p (as further on p HOME PAGE OF MIKLÓS RÁSONYI Miklós Rásonyi . Alfréd Rényi Institute of Mathematics Reáltanoda utca 13-15. Budapest 1053, Hungary. E-mail: mysurname.mygivenname@renyi.hu ON SOME PROBLEMS OF A STATISTICAL GROUP-THEORY. I Z. Wahrscheinlichkeitstheorie verw. Geb. 4, 175-186 (1965) On Some Problems of a Statistical Group-Theory. I BY P. ERDBS and P. TURIN 1. By statistical group-theory THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS 1 THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS PAUL ERD&, A. w. GOODMAN, AND LOUIS P&A 1. Introduction. Geometrically, a graph is a collection of points (or ON DECOMPOSITION OF GRAPHS ON DECOMPOSITION OF GRAPHS If a is regular, then aó = aby G. C. H. and the statement follows from Theorems 1 and 2 for finite and infinite a respectively. If a is singular thena::-S+, hence there is a regular a' satisfying max (y, b+) --a' < a. SOME PROBLEMS AND RESULTS ON THE IRRATIONALITY OF … 2 IRRATIONALITY OF THE SUM OF INFINITE SERIES lim supnk'rk = oo• (4) k=m Then a is a Liouville number. It is easy to see that Theorem 1 is best possible. It is well known and easy to see that for every A there is a sequence nk satisfying nk > A2k for every k > 0 but i I isrational.
THE HISTORY OF DEGENERATE (BIPARTITE) EXTREMAL GRAPH PROBLEMS Fu¨redi-Simonovits (FureSimSurvC) May15,2013 1 1. Introduction This survey describes the theory of Degenerate Extremal Graph Problems, themain results of the
MIKLÓS SIMONOVITS
Further Items; Obituaries on Paul Erdős (1913-1996) from the homepage of Peter Komjath Peter Paul Erdös and his mathematics. Papers from the International Conference held in memory of Paul Erdös in Budapest, July 4--11, 1999.GYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.hu HOME PAGE OF MIKLÓS RÁSONYI Miklós Rásonyi . Alfréd Rényi Institute of Mathematics Reáltanoda utca 13-15. Budapest 1053, Hungary. E-mail: mysurname.mygivenname@renyi.hu HOMEPAGE OF MIKLÓS ABÉRT Recent work M. Abért, T. Gelander and N. Nikolov, Rank, combinatorial cost and homology torsion growth in higher rank lattices M. Abért, A Spectral Strong Approximation theorem for measure preserving actions M. Abért, A. Thom and B. Virág, Benjamini-Schramm convergence and pointwise convergence of the spectral measure M. Abért, P. Csikvári and T. Hubai, Matching measure PROBLEMS AND RESULTS ON THE THEORY OF INTERPOLATION. I PROBLEMS AND RESULTS ON THE THEORY OF INTERPOLATION. I 383 By more complicated arguments we could prove the following stronger THEOREM 2. Let n > no(A, c, #, 8) be sufficiently large, -1 - x, < x2 < HOMEPAGE OF BALÁZS SZEGEDY Recent work. Higher order Fourier analysis: a theory of higher order structures in compact abelian groups, which proves general inverse theorems and regularity lemmas for Gowers uniformity norms. P. Candela, D. González-Sánchez, B. Szegedy. On nilspace systems and their morphisms. P. Candela, B. Szegedy. Nilspace factors for general uniformity seminorms, cubic ON THE ASYMPTOTIC BEHAVIOR OF LARGE PRIME FACTORS OF … pacific journal 0~ mathematics vol. 82, no. 2, 1979 on the asymptotic behavior of large prime factors of integers k. alladi and p. erd& A SIMPLE PROOF OF SANOV’S THEOREM* “main” — 2006/11/28 — 20:41 — page 3 — #3 A SIMPLE PROOF OF SANOV’S THEOREM 3 Remark 1. To make sure that Qn({x :Pˆx ∈0})is well defined, usually a UNSOLVED PROBLEMS HEPA3PELHEHHB1E FIPO&IEMBI 222 ERDÖS LANDAU. HARDY and LITTLEWOOD proved by BRUN'S method that A conjecture weaker than (I. 1.1) but stronger than (I. 1.3) would be: To every E > 0 there exists a yo so that for y > yo (I. 1.4) 70 + y) -n(x) < (1 + E) y log y* The replacement in (I. 1.3) of 2 by a smaller constant would be of greatLÁSZLÓ CSIRMAZ
This stellar icosi-dodecahedron had been in the CEU Computer Lab.I made it from green cardboard paper. It has a specially designed interior. Look at the pictures.ISTVAN_MIKLOS
A mathematician is a device for turning coffee into theorems. - Paul Erdős. Hobby The blues band where I used to play the bass 10 yearsago
INTRODUCTION
LANDAU’S PROBLEMS ON PRIMES 3 where C0 is the so-called twin prime constant, (2.6) C0 = Y p>2 µ 1− 1 (p−1)2 = 0.66016 . Here and later p (as further on p HOMEPAGE OF GABOR KUN Gabor Kun Email: lastname.firstname@renyi.mta.hu Address: MTA Alfred Renyi Institute of Mathematics Realtanoda utca 13-15. Budapest, Hungary, H-1053 CV Recent publications Gabor Kun: "On sofic approximations of Property (T) groups", arxiv Gabor Kun: "Expanders admit a Lipschitz subgraph with large girth", submitted, arxiv Gabor Kun and Daniel Dadush: "Lattice sparsifiers and the approximate HOMEPAGE OF BALÁZS SZEGEDY Balázs Szegedy. Reáltanoda utca 13-15. My main research areas are combinatorics and group theory. At the moment, I am working in various topics related to limits of discrete structures. This field is connected to combinatorics, ergodic theory and probability theory. Higher order Fourier analysis: a theory of higher order structures incompact
EXTREMAL PROBLEMS IN NUMBER THEORY EXTREMAL PROBLEMS IN NUMBER THEORY 183 (8) Ui (mod ni), 1 Si ,2 µ 1− 1 (p−1)2 = 0.66016 . Here and later p (as further on p HOMEPAGE OF GABOR KUN Gabor Kun Email: lastname.firstname@renyi.mta.hu Address: MTA Alfred Renyi Institute of Mathematics Realtanoda utca 13-15. Budapest, Hungary, H-1053 CV Recent publications Gabor Kun: "On sofic approximations of Property (T) groups", arxiv Gabor Kun: "Expanders admit a Lipschitz subgraph with large girth", submitted, arxiv Gabor Kun and Daniel Dadush: "Lattice sparsifiers and the approximate ON SOME PROBLEMS OF A STATISTICAL GROUP-THEORY. I Z. Wahrscheinlichkeitstheorie verw. Geb. 4, 175-186 (1965) On Some Problems of a Statistical Group-Theory. I BY P. ERDBS and P. TURIN 1. By statistical group-theory THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS 1 THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS PAUL ERD&, A. w. GOODMAN, AND LOUIS P&A 1. Introduction. Geometrically, a graph is a collection of points (or ON DECOMPOSITION OF GRAPHS ON DECOMPOSITION OF GRAPHS If a is regular, then aó = aby G. C. H. and the statement follows from Theorems 1 and 2 for finite and infinite a respectively. If a is singular thena::-S+, hence there is a regular a' satisfying max (y, b+) --a' < a. SOME PROBLEMS AND RESULTS ON THE IRRATIONALITY OF … 2 IRRATIONALITY OF THE SUM OF INFINITE SERIES lim supnk'rk = oo• (4) k=m Then a is a Liouville number. It is easy to see that Theorem 1 is best possible. It is well known and easy to see that for every A there is a sequence nk satisfying nk > A2k for every k > 0 but i I isrational.
MIKLÓS SIMONOVITS
Further Items; Obituaries on Paul Erdős (1913-1996) from the homepage of Peter Komjath Peter Paul Erdös and his mathematics. Papers from the International Conference held in memory of Paul Erdös in Budapest, July 4--11, 1999. THE HISTORY OF DEGENERATE (BIPARTITE) EXTREMAL GRAPH PROBLEMS Fu¨redi-Simonovits (FureSimSurvC) May15,2013 1 1. Introduction This survey describes the theory of Degenerate Extremal Graph Problems, themain results of the
GYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.hu HOMEPAGE OF MIKLÓS ABÉRT Miklós Abért. miklos.abert at renyi.mta.hu. MTA Alfréd Rényi Institute of Mathematics. Reáltanoda utca 13-15. H-1053 Budapest, Hungary. Research interest. I am interested in measured and asymptotic group theory, in particular spectral theory of graphs and groups, local sampling convergence, graph polynomials, stochastic processes ongroups
INTRODUCTION
LANDAU’S PROBLEMS ON PRIMES 3 where C0 is the so-called twin prime constant, (2.6) C0 = Y p>2 µ 1− 1 (p−1)2 = 0.66016 . Here and later p (as further on p HOMEPAGE OF GABOR KUN Gabor Kun Email: lastname.firstname@renyi.mta.hu Address: MTA Alfred Renyi Institute of Mathematics Realtanoda utca 13-15. Budapest, Hungary, H-1053 CV Recent publications Gabor Kun: "On sofic approximations of Property (T) groups", arxiv Gabor Kun: "Expanders admit a Lipschitz subgraph with large girth", submitted, arxiv Gabor Kun and Daniel Dadush: "Lattice sparsifiers and the approximate ON SOME PROBLEMS OF A STATISTICAL GROUP-THEORY. I Z. Wahrscheinlichkeitstheorie verw. Geb. 4, 175-186 (1965) On Some Problems of a Statistical Group-Theory. I BY P. ERDBS and P. TURIN 1. By statistical group-theory THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS 1 THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS PAUL ERD&, A. w. GOODMAN, AND LOUIS P&A 1. Introduction. Geometrically, a graph is a collection of points (or ON DECOMPOSITION OF GRAPHS ON DECOMPOSITION OF GRAPHS If a is regular, then aó = aby G. C. H. and the statement follows from Theorems 1 and 2 for finite and infinite a respectively. If a is singular thena::-S+, hence there is a regular a' satisfying max (y, b+) --a' < a. SOME PROBLEMS AND RESULTS ON THE IRRATIONALITY OF … 2 IRRATIONALITY OF THE SUM OF INFINITE SERIES lim supnk'rk = oo• (4) k=m Then a is a Liouville number. It is easy to see that Theorem 1 is best possible. It is well known and easy to see that for every A there is a sequence nk satisfying nk > A2k for every k > 0 but i I isrational.
MIKLÓS SIMONOVITS
Further Items; Obituaries on Paul Erdős (1913-1996) from the homepage of Peter Komjath Peter Paul Erdös and his mathematics. Papers from the International Conference held in memory of Paul Erdös in Budapest, July 4--11, 1999. THE HISTORY OF DEGENERATE (BIPARTITE) EXTREMAL GRAPH PROBLEMS Fu¨redi-Simonovits (FureSimSurvC) May15,2013 1 1. Introduction This survey describes the theory of Degenerate Extremal Graph Problems, themain results of the
GYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.hu HOMEPAGE OF MIKLÓS ABÉRT Miklós Abért. miklos.abert at renyi.mta.hu. MTA Alfréd Rényi Institute of Mathematics. Reáltanoda utca 13-15. H-1053 Budapest, Hungary. Research interest. I am interested in measured and asymptotic group theory, in particular spectral theory of graphs and groups, local sampling convergence, graph polynomials, stochastic processes ongroups
HOME PAGE OF MIKLÓS RÁSONYI Miklós Rásonyi . Alfréd Rényi Institute of Mathematics Reáltanoda utca 13-15. Budapest 1053, Hungary. E-mail: mysurname.mygivenname@renyi.huVIKTOR HARANGI
with B. Gerencsér: Too Acute to Be True: The story of acute sets The American Mathematical Monthly, 126 (2019), no.10, 905-914. The article received the 2020 Halmos–Ford award. HOMEPAGE OF BALÁZS SZEGEDY Balázs Szegedy. Reáltanoda utca 13-15. My main research areas are combinatorics and group theory. At the moment, I am working in various topics related to limits of discrete structures. This field is connected to combinatorics, ergodic theory and probability theory. Higher order Fourier analysis: a theory of higher order structures incompact
UNSOLVED PROBLEMS HEPA3PELHEHHB1E FIPO&IEMBI 222 ERDÖS LANDAU. HARDY and LITTLEWOOD proved by BRUN'S method that A conjecture weaker than (I. 1.1) but stronger than (I. 1.3) would be: To every E > 0 there exists a yo so that for y > yo (I. 1.4) 70 + y) -n(x) < (1 + E) y log y* The replacement in (I. 1.3) of 2 by a smaller constant would be of great ON THE ASYMPTOTIC BEHAVIOR OF LARGE PRIME FACTORS OF … pacific journal 0~ mathematics vol. 82, no. 2, 1979 on the asymptotic behavior of large prime factors of integers k. alladi and p. erd& A SIMPLE PROOF OF SANOV’S THEOREM* “main” — 2006/11/28 — 20:41 — page 3 — #3 A SIMPLE PROOF OF SANOV’S THEOREM 3 Remark 1. To make sure that Qn({x :Pˆx ∈0})is well defined, usually aLÁSZLÓ CSIRMAZ
László Csirmaz. I do research in Set Theory, Combinatorics, and Mathematical Logic. My favourite subject, however, is Cryptography, especially secret sharing. You can write to me at . This stellar icosi-dodecahedron had been in the CEU Computer Lab . I made it from green cardboard paper.ANDRAS NEMETHI
ANDRÁS NÉMETHI - HOME PAGE Publication List. Curriculum VitaeGYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.hu HOMEPAGE OF MIKLÓS ABÉRT Miklós Abért. miklos.abert at renyi.mta.hu. MTA Alfréd Rényi Institute of Mathematics. Reáltanoda utca 13-15. H-1053 Budapest, Hungary. Research interest. I am interested in measured and asymptotic group theory, in particular spectral theory of graphs and groups, local sampling convergence, graph polynomials, stochastic processes ongroups
INTRODUCTION
LANDAU’S PROBLEMS ON PRIMES 3 where C0 is the so-called twin prime constant, (2.6) C0 = Y p>2 µ 1− 1 (p−1)2 = 0.66016 . Here and later p (as further on p HOMEPAGE OF GABOR KUN Gabor Kun Email: lastname.firstname@renyi.mta.hu Address: MTA Alfred Renyi Institute of Mathematics Realtanoda utca 13-15. Budapest, Hungary, H-1053 CV Recent publications Gabor Kun: "On sofic approximations of Property (T) groups", arxiv Gabor Kun: "Expanders admit a Lipschitz subgraph with large girth", submitted, arxiv Gabor Kun and Daniel Dadush: "Lattice sparsifiers and the approximate ON SOME PROBLEMS OF A STATISTICAL GROUP-THEORY. I Z. Wahrscheinlichkeitstheorie verw. Geb. 4, 175-186 (1965) On Some Problems of a Statistical Group-Theory. I BY P. ERDBS and P. TURIN 1. By statistical group-theory THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS 1 THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS PAUL ERD&, A. w. GOODMAN, AND LOUIS P&A 1. Introduction. Geometrically, a graph is a collection of points (or ON DECOMPOSITION OF GRAPHS ON DECOMPOSITION OF GRAPHS If a is regular, then aó = aby G. C. H. and the statement follows from Theorems 1 and 2 for finite and infinite a respectively. If a is singular thena::-S+, hence there is a regular a' satisfying max (y, b+) --a' < a. SOME PROBLEMS AND RESULTS ON THE IRRATIONALITY OF … 2 IRRATIONALITY OF THE SUM OF INFINITE SERIES lim supnk'rk = oo• (4) k=m Then a is a Liouville number. It is easy to see that Theorem 1 is best possible. It is well known and easy to see that for every A there is a sequence nk satisfying nk > A2k for every k > 0 but i I isrational.
MIKLÓS SIMONOVITS
Further Items; Obituaries on Paul Erdős (1913-1996) from the homepage of Peter Komjath Peter Paul Erdös and his mathematics. Papers from the International Conference held in memory of Paul Erdös in Budapest, July 4--11, 1999. THE HISTORY OF DEGENERATE (BIPARTITE) EXTREMAL GRAPH PROBLEMS Fu¨redi-Simonovits (FureSimSurvC) May15,2013 1 1. Introduction This survey describes the theory of Degenerate Extremal Graph Problems, themain results of the
GYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.hu HOMEPAGE OF MIKLÓS ABÉRT Miklós Abért. miklos.abert at renyi.mta.hu. MTA Alfréd Rényi Institute of Mathematics. Reáltanoda utca 13-15. H-1053 Budapest, Hungary. Research interest. I am interested in measured and asymptotic group theory, in particular spectral theory of graphs and groups, local sampling convergence, graph polynomials, stochastic processes ongroups
INTRODUCTION
LANDAU’S PROBLEMS ON PRIMES 3 where C0 is the so-called twin prime constant, (2.6) C0 = Y p>2 µ 1− 1 (p−1)2 = 0.66016 . Here and later p (as further on p HOMEPAGE OF GABOR KUN Gabor Kun Email: lastname.firstname@renyi.mta.hu Address: MTA Alfred Renyi Institute of Mathematics Realtanoda utca 13-15. Budapest, Hungary, H-1053 CV Recent publications Gabor Kun: "On sofic approximations of Property (T) groups", arxiv Gabor Kun: "Expanders admit a Lipschitz subgraph with large girth", submitted, arxiv Gabor Kun and Daniel Dadush: "Lattice sparsifiers and the approximate ON SOME PROBLEMS OF A STATISTICAL GROUP-THEORY. I Z. Wahrscheinlichkeitstheorie verw. Geb. 4, 175-186 (1965) On Some Problems of a Statistical Group-Theory. I BY P. ERDBS and P. TURIN 1. By statistical group-theory THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS 1 THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS PAUL ERD&, A. w. GOODMAN, AND LOUIS P&A 1. Introduction. Geometrically, a graph is a collection of points (or ON DECOMPOSITION OF GRAPHS ON DECOMPOSITION OF GRAPHS If a is regular, then aó = aby G. C. H. and the statement follows from Theorems 1 and 2 for finite and infinite a respectively. If a is singular thena::-S+, hence there is a regular a' satisfying max (y, b+) --a' < a. SOME PROBLEMS AND RESULTS ON THE IRRATIONALITY OF … 2 IRRATIONALITY OF THE SUM OF INFINITE SERIES lim supnk'rk = oo• (4) k=m Then a is a Liouville number. It is easy to see that Theorem 1 is best possible. It is well known and easy to see that for every A there is a sequence nk satisfying nk > A2k for every k > 0 but i I isrational.
MIKLÓS SIMONOVITS
Further Items; Obituaries on Paul Erdős (1913-1996) from the homepage of Peter Komjath Peter Paul Erdös and his mathematics. Papers from the International Conference held in memory of Paul Erdös in Budapest, July 4--11, 1999. THE HISTORY OF DEGENERATE (BIPARTITE) EXTREMAL GRAPH PROBLEMS Fu¨redi-Simonovits (FureSimSurvC) May15,2013 1 1. Introduction This survey describes the theory of Degenerate Extremal Graph Problems, themain results of the
GYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.hu HOMEPAGE OF MIKLÓS ABÉRT Miklós Abért. miklos.abert at renyi.mta.hu. MTA Alfréd Rényi Institute of Mathematics. Reáltanoda utca 13-15. H-1053 Budapest, Hungary. Research interest. I am interested in measured and asymptotic group theory, in particular spectral theory of graphs and groups, local sampling convergence, graph polynomials, stochastic processes ongroups
HOME PAGE OF MIKLÓS RÁSONYI Miklós Rásonyi . Alfréd Rényi Institute of Mathematics Reáltanoda utca 13-15. Budapest 1053, Hungary. E-mail: mysurname.mygivenname@renyi.huVIKTOR HARANGI
with B. Gerencsér: Too Acute to Be True: The story of acute sets The American Mathematical Monthly, 126 (2019), no.10, 905-914. The article received the 2020 Halmos–Ford award. HOMEPAGE OF BALÁZS SZEGEDY Balázs Szegedy. Reáltanoda utca 13-15. My main research areas are combinatorics and group theory. At the moment, I am working in various topics related to limits of discrete structures. This field is connected to combinatorics, ergodic theory and probability theory. Higher order Fourier analysis: a theory of higher order structures incompact
UNSOLVED PROBLEMS HEPA3PELHEHHB1E FIPO&IEMBI 222 ERDÖS LANDAU. HARDY and LITTLEWOOD proved by BRUN'S method that A conjecture weaker than (I. 1.1) but stronger than (I. 1.3) would be: To every E > 0 there exists a yo so that for y > yo (I. 1.4) 70 + y) -n(x) < (1 + E) y log y* The replacement in (I. 1.3) of 2 by a smaller constant would be of great ON THE ASYMPTOTIC BEHAVIOR OF LARGE PRIME FACTORS OF … pacific journal 0~ mathematics vol. 82, no. 2, 1979 on the asymptotic behavior of large prime factors of integers k. alladi and p. erd& A SIMPLE PROOF OF SANOV’S THEOREM* “main” — 2006/11/28 — 20:41 — page 3 — #3 A SIMPLE PROOF OF SANOV’S THEOREM 3 Remark 1. To make sure that Qn({x :Pˆx ∈0})is well defined, usually aLÁSZLÓ CSIRMAZ
László Csirmaz. I do research in Set Theory, Combinatorics, and Mathematical Logic. My favourite subject, however, is Cryptography, especially secret sharing. You can write to me at . This stellar icosi-dodecahedron had been in the CEU Computer Lab . I made it from green cardboard paper.ANDRAS NEMETHI
ANDRÁS NÉMETHI - HOME PAGE Publication List. Curriculum VitaeGYULA O. H. KATONA
Address: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest, Reáltanoda u. 13-15. H-1364 Budapest, P. O. Box: 127 Phone: (36-1) 483-8318, (36-1) 483-8300 Fax: (36-1) 483-8333 e-mail:ohkatona@renyi.huohkatona@renyi.huINTRODUCTION
LANDAU’S PROBLEMS ON PRIMES 3 where C0 is the so-called twin prime constant, (2.6) C0 = Y p>2 µ 1− 1 (p−1)2 = 0.66016 . Here and later p (as further on p HOMEPAGE OF GABOR KUN Gabor Kun Email: lastname.firstname@renyi.mta.hu Address: MTA Alfred Renyi Institute of Mathematics Realtanoda utca 13-15. Budapest, Hungary, H-1053 CV Recent publications Gabor Kun: "On sofic approximations of Property (T) groups", arxiv Gabor Kun: "Expanders admit a Lipschitz subgraph with large girth", submitted, arxiv Gabor Kun and Daniel Dadush: "Lattice sparsifiers and the approximate ON SOME PROBLEMS OF A STATISTICAL GROUP-THEORY. I Z. Wahrscheinlichkeitstheorie verw. Geb. 4, 175-186 (1965) On Some Problems of a Statistical Group-Theory. I BY P. ERDBS and P. TURIN 1. By statistical group-theory THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS 1 THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS PAUL ERD&, A. w. GOODMAN, AND LOUIS P&A 1. Introduction. Geometrically, a graph is a collection of points (or RAMSEY-MINIMAL GRAPHS FOR THE PAIR STAR, RAMSEY-MINIMAL GRAPHS 267 PROOF of Theorem 1. To shorten the notation, V Ga will be denoted by W, and aEA since we will only be interested in the degree of vertices in the blue graph, d(F),, will be written dF throughout this proof. SOME INTERSECTION PROPERTIES OF RANDOM WALK PATHS* SOME INTERSECTION PROPERTIES oF RANDoM WALK PATHS 235 Similarly one can prove LEMMA 6. If o3(n) is the distance from the origin at the ntt1 step of a random walk in 3-space, then there exist constants c,,", cj' such that cs I + c ,' ON SOME OF MY CONJECTURES IN NUMBER THEORY AND by (log n) c . This,i£ true,is easily seen to be best possible. More generally denote by F(n) the smallest integer if it exists for which every integer u2 µ 1− 1 (p−1)2 = 0.66016 . Here and later p (asfurther on p
HOMEPAGE OF GABOR KUN Gabor Kun Email: lastname.firstname@renyi.mta.hu Address: MTA Alfred Renyi Institute of Mathematics Realtanoda utca 13-15. Budapest, Hungary, H-1053 CV Recent publications Gabor Kun: "On sofic approximations of Property (T) groups", arxiv Gabor Kun: "Expanders admit a Lipschitz subgraph with large girth", submitted, arxiv Gabor Kun and Daniel Dadush: "Lattice sparsifiers and the approximate ON SOME PROBLEMS OF A STATISTICAL GROUP-THEORY. I Z. Wahrscheinlichkeitstheorie verw. Geb. 4, 175-186 (1965) On Some Problems of a Statistical Group-Theory. I BY P. ERDBS and P. TURIN 1. By statistical group-theory THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS 1 THE REPRESENTATION OF A GRAPH BY SET INTERSECTIONS PAUL ERD&, A. w. GOODMAN, AND LOUIS P&A 1. Introduction. Geometrically, a graph is a collection of points (or RAMSEY-MINIMAL GRAPHS FOR THE PAIR STAR, RAMSEY-MINIMAL GRAPHS 267 PROOF of Theorem 1. To shorten the notation, V Ga will be denoted by W, and aEA since we will only be interested in the degree of vertices in the blue graph, d(F),, will be written dF throughout this proof. SOME INTERSECTION PROPERTIES OF RANDOM WALK PATHS* SOME INTERSECTION PROPERTIES oF RANDoM WALK PATHS 235 Similarly one can prove LEMMA 6. If o3(n) is the distance from the origin at the ntt1 step of a random walk in 3-space, then there exist constants c,,", cj' such that cs I + c ,' ON SOME OF MY CONJECTURES IN NUMBER THEORY AND by (log n) c . This,i£ true,is easily seen to be best possible. More generally denote by F(n) the smallest integer if it exists for whichevery integer u
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