Let d(N) (resp. p(N)) be the number of summands in the determinant (resp. permanent) of an N x 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.

ON THE COEFFICIENTS OF THE PERMANENT AND THE DETERMINANT OF A CIRCULANT MATRIX. APPLICATIONS

Emilia Mezzetti;
2019-01-01

Abstract

Let d(N) (resp. p(N)) be the number of summands in the determinant (resp. permanent) of an N x 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.
2019
5-nov-2018
Pubblicato
http://www.ams.org/journals/proc/2019-147-02/S0002-9939-2018-14296-3/
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2935994
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