The number of equivalence classes of symmetric sign patterns

Peter J. Cameron; Charles R. Johnson

doi:10.1016/j.disc.2004.10.029

The number of equivalence classes of symmetric sign patterns

Peter J. Cameron^*, Charles R. Johnson

^*Corresponding author for this work

Centre for Interdisciplinary Research in Computational Algebra

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

This paper shows that the number of sign patterns of totally non-zero symmetric n-by-n matrices, up to conjugation by permutation and signature matrices and negation, is equal to the number of unlabelled graphs on n vertices.

Original language	English
Pages (from-to)	3074-3077
Number of pages	4
Journal	Discrete Mathematics
Volume	306
Issue number	23 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.disc.2004.10.029
Publication status	Published - 6 Dec 2006

Keywords

Duality
Enumeration
Sign pattern
Symmetric matrix

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10.1016/j.disc.2004.10.029

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title = "The number of equivalence classes of symmetric sign patterns",

abstract = "This paper shows that the number of sign patterns of totally non-zero symmetric n-by-n matrices, up to conjugation by permutation and signature matrices and negation, is equal to the number of unlabelled graphs on n vertices.",

keywords = "Duality, Enumeration, Sign pattern, Symmetric matrix",

author = "Cameron, {Peter J.} and Johnson, {Charles R.}",

year = "2006",

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AU - Cameron, Peter J.

AU - Johnson, Charles R.

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N2 - This paper shows that the number of sign patterns of totally non-zero symmetric n-by-n matrices, up to conjugation by permutation and signature matrices and negation, is equal to the number of unlabelled graphs on n vertices.

AB - This paper shows that the number of sign patterns of totally non-zero symmetric n-by-n matrices, up to conjugation by permutation and signature matrices and negation, is equal to the number of unlabelled graphs on n vertices.

KW - Duality

KW - Enumeration

KW - Sign pattern

KW - Symmetric matrix

U2 - 10.1016/j.disc.2004.10.029

DO - 10.1016/j.disc.2004.10.029

M3 - Article

AN - SCOPUS:33750399078

SN - 0012-365X

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SP - 3074

EP - 3077

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 23 SPEC. ISS.

ER -

The number of equivalence classes of symmetric sign patterns

Abstract

Keywords

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