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SumTopo 2001, Sixteenth Summer Conference on Topology and its Applications
July 18-21, 2001
City College of CUNY
New York, NY, USA

Organizers
Ralph Kopperman (City College, CUNY), Susan Andima (CW Post College, LIU), Gerald Itzkowitz (Queens College, CUNY), Prabudh Misra (College of Staten Island, CUNY), Shelly Rothman (CW Post College, LIU), Aaron Todd (Baruch College, CUNY)

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Infinite image partition regular matrices
by
Dona Strauss
University of Hull
Coauthors: N. Hindman, I. Leader

A finite or infinite matrix A is image partition regular provided that, whenever N is finitely coloured, there exists [x\vec], with entries in N, such that all the entries of A[x\vec] are monochrome. The properties of finite image partition regular matrices are well known; but infinite image partition regular matrices have scarcely been studied. However, interesting results about these can be obtained by using the algebra of \betaN. For example, one can prove that, given any finite colouring of N, there are infinite sequences <xn > and <yn > in N such that all numbers of the form xm+3xn or -ym+4yn, with m < n, have the same colour.

Infinite image partition regular matrices

Date received: May 17, 2001

Copyright © 2001 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 # cagw-64.