Infinite Image Partition Regular Matrices - Solution in C-sets
نویسندگان
چکیده
منابع مشابه
Infinite Partition Regular Matrices: Solutions in Central Sets
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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Hindman and Leader first investigated Ramsey theoretic properties near 0 for dense subsemigroups of (R,+). Following them, the notion of image partition regularity near zero for matrices was introduced by De and Hindman. It was also shown there that like image partition regularity over N, the main source of infinite image partition regular matrices near zero are Milliken–Taylor matrices. But ex...
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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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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 u × v matrix A is image partition regular provided that, whenever N is finitely colored, there is some ~x ∈ N with all entries of A~x monochrome. Image partition regular matrices are a natural way of representing some of the classic theorems of Ramsey Theory, including theorems of Hilbert, Schur, and van der Waerden. ∗This author acknowledges support received from the National Science Foundat...
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ژورنال
عنوان ژورنال: Bulletin of the Brazilian Mathematical Society, New Series
سال: 2020
ISSN: 1678-7544,1678-7714
DOI: 10.1007/s00574-020-00201-0