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Evaluation of Permanents

Published online by Cambridge University Press:  20 January 2009

Henryk Minc
Henryk Minc
Affiliation:
University of CaliforniaSanta Barbara
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The permanent of an m x n matrix A = (aij), m ≤ n, is defined by

where the summation is over all one-to-one functions σ from {1, … , m} to { 1, …, n}. In other words, the permanent of A is the sum of all the diagonal products of A, that is, all the products of m entries of A no two of which lie in the same row or in the same column. Thus the permanent of A may be evaluated by first multiplying all the row sums of A and then subtracting from the product all terms that contain as factors two or more entries from the same column of A. This is the idea behind the formulas of Binet and of Ryser.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 1 , February 1979 , pp. 27 - 32
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

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(4) Ryser, H. J., Combinatorial Mathematics (Carus Math. Monograph No. 14, 1963).CrossRefGoogle Scholar