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arXiv · 1806.05905

On the Coefficients of the Permanent and the Determinant of a Circulant Matrix. Applications

Liena Colarte·Emilia Mezzetti·Rosa Maria Miró-Roig·Martí Salat
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Abstract

Let $d(N )$ (resp. $p(N )$) be the number of summands in the determinant (resp. permanent) of an $N\times N$ circulant matrix $A = (a_{ij} )$ given by $a_{ij} = X_{i+j}$ where $i + j$ should be considered $\mod N$ . This short note is devoted to prove that $d(N ) = p(N )$ if and only if $N$ is a prime power. We then give an application to homogeneous monomial ideals failing the Weak Lefschetz property.

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Liena Colarte, Emilia Mezzetti, Rosa Maria Miró-Roig, Martí Salat. 2018-06-15. On the Coefficients of the Permanent and the Determinant of a Circulant Matrix. Applications. https://arxiv.org/abs/1806.05905

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