Elsevier

Discrete Mathematics

Volume 309, Issue 10, 28 May 2009, Pages 3219-3232
Discrete Mathematics

Image partition regularity near zero

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Abstract

Many of the classical results of Ramsey Theory are naturally stated in terms of image partition regularity of matrices. Many characterizations are known of image partition regularity over N and other subsemigroups of (R,+). We study several notions of image partition regularity near zero for both finite and infinite matrices, and establish relationships which must hold among these notions.

Keywords

Ramsey Theory
Image partition regular matrix
Central Sets Theorem

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