On the Matrix-Element Expansion of a Circulant Determinant

Jerome Malenfant

On the Matrix-Element Expansion of a Circulant Determinant

Number Theory 2015-04-22 v5

Authors: Jerome Malenfant

Abstract

The determinant of an $N \times N$ circulant matrix $M = {\rm CIRC}[x_0, x_1, ..., x_{N-1}$ ] 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.

Keywords

circulant determinant matrix-element expansion generating function restricted partition function mod-N partition binomial coefficient

Cite

@article{arxiv.1502.06012,
  title  = {On the Matrix-Element Expansion of a Circulant Determinant},
  author = {Jerome Malenfant},
  journal= {arXiv preprint arXiv:1502.06012},
  year   = {2015}
}

Comments

Corrected a misprint in the statement of Lemma I

On the Matrix-Element Expansion of a Circulant Determinant

Abstract

Keywords

Cite

Comments

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