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A Remark on a Theorem of M. Hall

Published online by Cambridge University Press:  20 November 2018

Henryk Minc
Henryk Minc*
Affiliation:
University of California, Santa Barbara
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Let A = (aij) be an m×n (0, 1)-matrix, m≤n. The permanent of A is defined by

where the summation is over all one-one functions σ:{1, 2, . . . , m}→{1, 2, . . . , n}. If A is regarded as the incidence matrix of a configuration of m subsets of an n-set, then Per (A) is the number of systems of distinct representatives in the configuration.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 547 - 548
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Hall, M. Jr.=, Distinct representatives of subsets, Bull. Amer. Math. Soc. 54 (1948), 922-926.Google Scholar
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3. M. Marcus, and Mine, H., A survey of matrix theory and matrix inequalities, Boston, 1964 p. 97.Google Scholar
4. Ostrand, P. A., Systems of distinct representatives, II, J. Math. Anal. Appl. 32 (1970), 1-4.Google Scholar
5. Rado, R., On the number of systems of distinct representatives, J. London Math. Soc. 42 (1967), 107-109.Google Scholar