Universally Image Partition Regularity
نویسندگان
چکیده
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 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.
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If u, v ∈ N, A is a u × v matrix with entries from Q, and ~b ∈ Q, then (A,~b ) determines an affine transformation from Q to Q by ~x 7→ A~x + ~b. In 1933 and 1943 Richard Rado determined precisely when such transformations are kernel partition regular over N, Z, or Q, meaning that whenever the nonzero elements of the relevant set are partitioned into finitely many cells, there is some element o...
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We show that many of the natural analogues of known characterizations of image partition regularity and weak image partition regularity of matrices with rational entries over the integers are valid for matrices with real entries over the reals.
متن کاملImage partition regularity of matrices near 0 with real entries
We prove that many of the known results regarding image partition regularity and image partition regularity near zero for finite and infinite matrices with rational or integer entries have natural analogues for matrices with real entries over the reals, extending work by N. Hindman.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2008
ISSN: 1077-8926
DOI: 10.37236/865