On the Matrix-Element Expansion of a Circulant Determinant

2015/02/20 by Jerome Malenfant, Malenfant, Jerome · 1 citation
Computer Science · Mathematics · #15A15 #15B05 #FOS: Mathematics #Matrix Theory and Algorithms #Number Theory (math.NT) #math.NT #msc:15A15 #msc:15B05

paper · pdf · doi:10.48550/arxiv.1502.06012

Corrected a misprint in the statement of Lemma I

openalex publication_date 2015/02/20 · arxiv created 2015/04/21 · arxiv updated 2015/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The determinant of an N × N circulant matrix M = \rm CIRC[x₀, x₁, ..., x_N-1] can be expanded in the form det ~M= ∑ C_a₀ a₁ ...a_N-1 x_a0 x_a1...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.

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