Extensions of Infinite Partition Regular Systems
نویسندگان
چکیده
منابع مشابه
Extensions of Infinite Partition Regular Systems
A finite or infinite matrixA with rational entries (and only finitely many non-zero entries in each row) is called image partition regular if, whenever the natural numbers are finitely coloured, there is a vector x, with entries in the natural numbers, such that Ax is monochromatic. Many of the classical results of Ramsey theory are naturally stated in terms of image partition regularity. Our 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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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. In contrast to the finite case, infinite image partition regular matrices seem very hard to analyze: they do not enjoy the closure and consistency properties of the finite case, and it is diffic...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/4568