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On a Generalization of Szemerédi's Theorem
Author(s) -
Shkredov I. D.
Publication year - 2006
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1017/s0024611506015991
Subject(s) - mathematics , cardinality (data modeling) , generalization , combinatorics , constant (computer programming) , discrete mathematics , mathematical analysis , computer science , data mining , programming language
Let N be a natural number and A ⊂ [1, …, N] 2 be a set of cardinality at least N 2 /( log log N ) c is an absolute constant. We prove that A contains a triple {( k, m ), ( k + d , m ), ( k , m + d )}, where d > 0. This theorem is a two‐dimensional generalization of Szemerédi's theorem on arithmetic progressions. 2000 Mathematics Subject Classification 35J25, 37A15.