Balog, A., and Szemer edi, E. A statistical theorem of set addition. Combinatorica 14, 3 (1994), 263-268. Home/Search Document Not in Database Summary Related Articles Check |
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Ramsey Theory Applications - Rosta (2004) (Correct)
....a set of natural numbers with A(n) 402 # nlogn for n large enough, then there exists d such that d, 2d, 3d, # P(A) We mention here two very influential results from additive number theory using yet another sumset definition: A A = x y : x, y A . Balog and Szemeredi (1994) [25] proved that if A is a set of n integers and for some c 0 there are at least cn triples x, y, x y A, then there is a subset A # A such that c # n, # A # c ## n, where c # , c ## are positive constants depending only on c. This is a basic result with many possible ....
....der Waerden s theorem and Szemeredi s regularity lemma, both well known for extremely large constants and bounds. Instead he uses exponential sums like Roth, combined with modifications of Freiman s [117] theorem with Ruzsa s [220] new simple proof and modification of the Balog Szemeredi theorem [25]. r k (n) denotes the largest cardinality of a subset of [n] with no arithmetic sequence of lenght k. The lower bound of Behrend (1946) 33, 135] ne c # log n r 3 (n) has been applied to fast multiplication of matrices by Coppersmith and Winograd [73] 3 Geometry of fractals, Harmonic ....
A. Balog and E. Szemeredi, A statistical theorem of set addition, Combinatorica 14(3) (1994), 263--268.
SUMS versus PRODUCTS in Number Theory, Algebra and Erdös Geometry - Elekes (2001) (Correct)
.... Y j Cn then X [ Y is contained in an arithmetic GP G 2 G d ;C jXj , where d = d (C) and C = C (C) do not depend on n. Remark 1.4 Theorem 1.3 remains valid in any torsion free Abelian group. A statistical version of this result was found by Balog and Szemer edi in [4]. Let X be a subset of the reals or the complex numbers and E a set of unordered pairs of X (i.e. the edge set of an undirected graph H(X;E) on vertex set X) Put X E X def = fx 0 x 00 ; x 0 ; x 00 ) 2 Eg: Also, X E Y can be de ned similarly for bipartite graphs H(X;Y;E) on ....
....numbers and E a set of unordered pairs of X (i.e. the edge set of an undirected graph H(X;E) on vertex set X) Put X E X def = fx 0 x 00 ; x 0 ; x 00 ) 2 Eg: Also, X E Y can be de ned similarly for bipartite graphs H(X;Y;E) on vertex sets X , Y . Theorem 1. 5 (Balog Szemer edi [4]) If jEj jX j 2 and jX EX j CjX j then some jX j elements of X are contained in an arithmetic GP G 2 G d ;C jXj , where d = d (C; C = C (C; and = C; do not depend on jX j. Their proof is based upon Szemer edi s famous Regularity ....
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Antal Balog and Endre Szemeredi. A statistical theorem of set addition. Combinatorica, 14:263-268, 1994.
Szemerédi's Regularity Lemma and Its Applications in Graph.. - Komlós, Simonovits (1996) (Correct)
....new one; see [119, 108] In this paper we consider almost exclusively graph theoretical applications. However, the lemma was invented to solve number theoretical problems, and it is still used for this purpose also. For a recent number theoretical application see the paper of Balog and Szemer edi [9]. There are also many applications in combinatorial geometry. We refer the reader to a forthcoming book of Pach and Agarwal [96] and to the paper of Erdos, Makai and Pach [50] 8 1.7 Proof of the Regularity Lemma We only sketch the proof and emphasize its main features. First a measure ....
A. Balog, E. Szemer'edi, A statistical theorem of set-addition, Combinatorica 14 (1994), 263-268.
On Combinatorics of Projective Mappings - Elekes, Király (1998) (Correct)
....related to Abelian subgroups. 0 Introduction Freiman [5, 6] and Ruzsa [12, 13] studied subsets of R, for which jA Bj Cn, where jAj = jBj = n. They described the structure of A and B in terms of some natural generalizations of arithmetic progressions. Using their theorems, Balog Szemer edi [1] and Laczkovich Ruzsa [8] found some statistical versions. Their results extend to torsion free Abelian groups, as well. Generalizations to non Abelian groups were initiated by the first named author in [3, 4] where the one dimensional affine group was considered. The goal of this paper is to ....
Antal Balog and Endre Szemer'edi. A statistical theorem of set addition. Combinatorica, 14:263--268, 1994.
Fourier Analysis and Szemerédi's Theorem - Gowers (1998) (Correct)
....and D depend on C only. To relate Freiman s theorem to our problem, we consider the graph of the function OE, which we shall call Gamma. This is a subset of Z 2 N of size at most N which contains at least flN 3 quadruples (x; y; z; w) such that x y = z w. A theorem of Balog and Szemer edi [BS] now tells us that Gamma contains a subset X of size at least jN such that jX X j CjX j, with j and C constants that depend on fl (and hence ff) only. It is an easy exercise to formulate an appropriate version of Freiman s theorem for subsets of Z 2 (as we may regard X) and prove that it is ....
A. Balog and E. Szemer'edi, A statistical theorem of set addition, Combinatorica 14 (1994), 263-268.
Ramsey Theory Applications - Vera Rosta Dept (Correct)
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Balog, A., and Szemer edi, E. A statistical theorem of set addition. Combinatorica 14, 3 (1994), 263-268.
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