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A Note on Permanents

Published online by Cambridge University Press:  20 November 2018

Morton Abramson
Morton Abramson*
Affiliation:
York University, Toronto, Ontario
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Let A = (aij) be an m × n matrix and let K = {s1, …, sk} be a k-subset from {1, 2, …, n}. For 0≤t≤k≤n define the (t, K)-permanent of A to be

(1)

the summation taken over all m-tuples (i1, i2, …, im) (repetitions allowed) of 1, 2, …, n each containing exactly t distinct entries from K and any number of distinct entries from the remaining n-k integers. For example, (4, 4, 7, 1, 1, 2), (4, 4, 6, 6, 6, 5) are 6-tuples, each containing exactly two distinct entries from K={2, 4, 5} for n ≥ 7.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 1 - 4
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Marcus, Marvin and Mine, Henryk, Permanents, Amer. Math. Monthly, 72(1965), 577-591.Google Scholar
2. Riordan, J., An introduction to combinatorial analysis, Wiley, New York, 1958.Google Scholar
3. Ryser, Herbert John, Combinatorial mathematics, Carus Math. Monograph No. 14, 1963.Google Scholar