On the Matrix-Element Expansion of a Circulant Determinant

Jerome Malenfant

paper

On the Matrix-Element Expansion of a Circulant Determinant

arXiv:1502.06012

Abstract

The determinant of an $N \times N$ circulant matrix $M = CIRC [x_{0}, x_{1}, ..., x_{N - 1}$ ] can be expanded in the form det $M = \sum C_{a_{0} a_{1} ... a_{N - 1}} x_{a_{0}} x_{a_{1}} ... x_{a_{N - 1}}$ . By using the generating function of a restricted, mod- $N$ partition function, we derive a formula for the coefficients in this expansion as finite sums over products of binomial coefficients with integer variables.

Corrected a misprint in the statement of Lemma I

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