Hostname: page-component-7dd5485656-c8zdz Total loading time: 0 Render date: 2025-10-31T06:46:09.370Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Information

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
2. Mann, H. B. and Ryser, H. J., Systems of distinct representatives, Amer. Math. Monthly 60 (1953), 397-401.Google Scholar
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