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Image partition regular matrices
by
Dona Strauss
Hull University
Coauthors: Neil Hindman, Imre Leader
A finite or infinite matrix A with rational entries is said to be image partition regular if, given any finite colouring of the positive integers, there is a vector [x\vec] with positive integral entries, for which the entries of A[x\vec] are monochrome. Many theorems in combinatorics, such as van der Waerden's Theorem or Hindman's Theorem, are equivalent to the statement that a particular matrix is image partition regular. I wish to discuss some old and some new results about matrices of this kind.
Date received: August 20, 1999
Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadg-10.