Image partition regularity near zero
نویسندگان
چکیده
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.
منابع مشابه
Matrices centrally image partition regular near 0
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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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...
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عنوان ژورنال:
- Discrete Mathematics
دوره 309 شماره
صفحات -
تاریخ انتشار 2009