The Knowlton-Graham partition problem

DOI10.1006/JCTA.1996.0015zbMATH Open0851.05007arXivmath/9502237OpenAlexW2001356323MaRDI QIDQ1906132

Donald E. Knuth

Publication date: 13 May 1996

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Abstract: A set partition technique that is useful for identifying wires in cables can be recast in the language of 0--1 matrices, thereby resolving an open problem stated by R.~L. Graham in Volume 1 of this journal. The proof involves a construction of 0--1 matrices having row and column sums without gaps.

Full work available at URL: https://arxiv.org/abs/math/9502237

zbMATH Keywords

symmetric matrix0-1 matricescolumn sumsKnowlton-Graham partitions

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17)

Related Items (1)

The mean-partition problem

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