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.
Titolo: | ON THE COEFFICIENTS OF THE PERMANENT AND THE DETERMINANT OF A CIRCULANT MATRIX. APPLICATIONS |
Autori: | |
Data di pubblicazione: | 2019 |
Data ahead of print: | 5-nov-2018 |
Stato di pubblicazione: | Pubblicato |
Rivista: | |
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. |
Handle: | http://hdl.handle.net/11368/2935994 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1090/proc/14296 |
URL: | http://www.ams.org/journals/proc/2019-147-02/S0002-9939-2018-14296-3/ |
Appare nelle tipologie: | 1.1 Articolo in Rivista |
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