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On the Coefficients of the Permanent and the Determinant of a Circulant Matrix. Applications by Colarte, Liena; Mezzetti, Emilia; Miró-Roig, Rosa Maria; Salat, Martí is a scholarly article available to read on EtoBox.

What is On the Coefficients of the Permanent and the Determinant of a Circulant Matrix. Applications about?

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.

Author

Colarte, Liena; Mezzetti, Emilia; Miró-Roig, Rosa Maria; Salat, Martí

Published

2018

Language

EN