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 / Colarte, L., Mezzetti, E., Miró-Roig, R.M., Salat, M.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 1088-6826. - STAMPA. - 147:2(2019), pp. 547-558. [10.1090/proc/14296]
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.| File | Dimensione | Formato | |
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