On a Generalization of Szemeredi's Theorem |
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| Authors: | Shkredov I D |
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| Institution: | Department of Mechanics and Mathematics, Moscow State University Leninskie Gory, Moscow, 119992, Russia ishkredov{at}rambler.ru, ishkredo{at}mech.math.msu.su |
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| Abstract: | Let N be a natural number and A  1, ..., N]2 be a set of cardinalityat least  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 generalizationof Szemerédi's theorem on arithmetic progressions. 2000Mathematics Subject Classification 35J25, 37A15. |
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