منابع مشابه
Multiply partition regular matrices
Let A be a finite matrix with rational entries. We say that A is doubly image partition regular if whenever the set N of positive integers is finitely coloured, there exists ~x such that the entries of A~x are all the same colour (or monochromatic) and also, the entries of ~x are monochromatic. Which matrices are doubly image partition regular? More generally, we say that a pair of matrices (A,...
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A finite or infinite matrix A is image partition regular provided that whenever N is finitely colored, there must be some ~x with entries from N such that all entries of A~x are in the same color class. Using the algebraic structure of the StoneČech compactification βN of N, along with a good deal of elementary combinatorics, we investigate the degree to which the known characterizations of fin...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2014
ISSN: 0012-365X
DOI: 10.1016/j.disc.2014.01.003