The number of terms in the permanent and the determinant of a generic circulant matrix

Details The number of terms in the permanent and the determinant of a generic circulant matrix The number of terms in the permanent and the determinant of a generic circulant matrix

2003-01-07

arxiv.org/abs/math/0301048v1

Mathematics

Combinatorics

6 pages; 1 figure

Scientific paper

Let A=(a_(ij)) be the generic n by n circulant matrix given by a_(ij)=x_(i+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). The proof uses symmetric functions.

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