منابع مشابه
Universally Image Partition Regularity
Many of the classical results of Ramsey Theory, for example Schur’s Theorem, van der Waerden’s Theorem, Finite Sums Theorem, 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,+). In this paper we introduce a new notion which we call universally image partition regular matri...
متن کاملPartition Regularity of Matrices
This is a survey of results on partition regularity of matrices, beginning with the classic results of Richard Rado on kernel partition regularity, continuing with the groundbreaking results of Walter Deuber on image partition regularity, and leading up to the present day. Included are the largely settled world of finite matrices and the mostly unknown world of infinite matrices.
متن کاملOpen Problems in Partition Regularity
A finite or infinite matrix A with rational entries is called partition regular if whenever the natural numbers are finitely coloured there is a monochromatic vector x with Ax = 0. Many of the classical theorems of Ramsey Theory may naturally be interpreted as assertions that particular matrices are partition regular. While in the finite case partition regularity is well understood, very little...
متن کاملImage partition regularity near zero
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.
متن کاملPartition regularity in the rationals
A system of homogeneous linear equations with integer coefficients is partition regular if, whenever the natural numbers are finitely coloured, the system has a monochromatic solution. The Finite Sums theorem provided the first example of an infinite partition regular system of equations. Since then, other such systems of equations have been found, but each can be viewed as a modification of th...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2020
ISSN: 1077-8926
DOI: 10.37236/7972