منابع مشابه
Partition and composition matrices: two matrix analogues of set partitions
This paper introduces two matrix analogues for set partitions; partition and composition matrices. These two analogues are the natural result of lifting the mapping between ascent sequences and integer matrices given in Dukes & Parviainen (2010). We prove that partition matrices are in one-to-one correspondence with inversion tables. Non-decreasing inversion tables are shown to correspond to pa...
متن کاملMultiply partition regular matrices
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,...
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 کاملMatrices 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...
متن کاملThe part-frequency matrices of a partition
A new combinatorial object is introduced, the part-frequency matrix sequence of a partition, which is elementary to describe and is naturally motivated by Glaisher’s bijection. We prove results that suggest surprising usefulness for such a simple tool, including the existence of a related statistic that realizes every possible Ramanujan-type congruence for the partition function. To further exh...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2011
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2011.02.001