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An Algorithm for the Permanent of Circulant Matrices

Published online by Cambridge University Press:  20 November 2018

Larry J. Cummings  and
Jennifer Seberry Wallis
Larry J. Cummings
Affiliation:
Faculty of Mathematics University of Waterloo Waterloo, OntarioN2L 3G1
Jennifer Seberry Wallis
Affiliation:
Institute of Advanced Studies Australian National University
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The permanent of an n ✕ n matrix A = (aij) is the matrix function

1

where the summation is over all permutations in the symmetric group, Sn. An n ✕ n matrix A is a circulant if there are scalars a1 …, an such that

2

where P is the n ✕ n permutation matrix corresponding to the cycle (12 … n) in Sn.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 67 - 70
Copyright
Copyright © Canadian Mathematical Society 1977

References

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