AMCA: Different shades of Gray: (n,m)-Gray codes and quasi-cubes by John Frederick Fink

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Horizons in Combinatorics/16th Shanks Lecture Series
May 21-24, 2001
Vanderbilt University
Nashville, TN, USA

Organizers
Paul Edelman, Mark Ellingham, Jonathan Farley, Mike Plummer, Jerry Spinrad

Different shades of Gray: (n, m)-Gray codes and quasi-cubes
by
John Frederick Fink
University of Michigan - Dearborn

For positive integers n and m with m < n, define an (n, m)-Gray code to be a listing of all bitstrings of length n in which consecutive strings differ in exactly m bits. Also, define the quasi-cube Q(n, m) to be the graph whose vertices are the bitstrings of length n, with two vertices adjacent if and only if they differ in exactly m bit positions. We discuss properties of Q(n, m) and show that (n, m)-Gray codes exist for all positive integers n and m for which m is odd and m < n.

Date received: April 18, 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 Mathematical Conference Abstracts. Document # cags-34.