The Number of Terms in the Permanent and the Determinant of a Generic Circulant Matrix

Authors:
Hugh Thomas
Affiliations:
Fields Institute, 222 College Street, Toronto ON, M5T 3J1, Canada. hthomas@fields.utoronto.ca
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2004

Citing 2
Cited 1

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Journal of Algebraic Combinatorics: An International Journal

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Abstract

Let A = (aij) be the generic n × n circulant matrix given by aij = xi + j, with subscripts on x interpreted mod n. Define d(n) (resp. p(n)) to be the number of terms in the determinant (resp. permanent) of A. The function p(n) is well-known and has several combinatorial interpretations. The function d(n), on the other hand, has not been studied previously. We show that when n is a prime power, d(n) = p(n).