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The Permanent Function

Published online by Cambridge University Press:  20 November 2018

Marvin Marcus  and
F. C. May
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Let X be an n-square matrix with elements in a field F. The permanent of X is defined by

1.1

where σ runs over the symmetric group of permutations on 1, 2, … , n. This function makes its appearance in certain combinatorial applications (13), and is involved in a conjecture of van der Waerden (6; 9). Certain formal properties of per (X) are known (1), and an old paper of Pólya (12) shows that for n > 2 one cannot multiply the elements of X by constants in any uniform way so as to convert the permanent into the determinant. In a subsequent paper we intend to investigate this problem for more general operations on X.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 177 - 189
Copyright
Copyright © Canadian Mathematical Society 1962

References

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