Infinite partition regular matrices |
| |
| Authors: | Walter A Deuber Neil Hindman Imre Leader Hanno Lefmann |
| |
| Institution: | (1) Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany;(2) Department of Mathematics, Howard University, 20059 Washington, D.C., USA;(3) Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, CB2 1SB Cambridge, England;(4) Fachbereich Informatik, LS II, Universität Dortmund, D-44221 Dortmund, Germany |
| |
| Abstract: | We consider infinite matrices with entries from (and only finitely many nonzero entries on any row). A matrixA is partition regular over provided that, whenever the set of positive integers is partitioned into finitely many classes there is a vector
with entries in such that all entries ofA
lie in the same cell of the partition. We show that, in marked contrast with the situation for finite matrices, there exists a finite partition of no cell of which contains solutions for all partition regular matrices and determine which of our pairs of matrices must always have solutions in the same cell of a partition. |
| |
| Keywords: | 05 D 10 |
| 本文献已被 SpringerLink 等数据库收录！ |
|
