On the coefficients of the permanent and the determinant of a circulant matrix: Applications

Let d(N) (resp., p(N)) be the number of summands in the determinant (resp., permanent) of an N × 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 proving that d(N) = p(N) if and only if N is a prime power. We then give an appl...

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Detalles Bibliográficos
Autores: Colarte, Liena, Mezzetti, Emilia, Miró-Roig, M., Salat, Martí
Tipo de recurso: artículo
Estado:Versión borrador
Fecha de publicación:2019
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/378033
Acceso en línea:http://hdl.handle.net/2072/378033
Access Level:acceso abierto
Palabra clave:Matemàtiques
51
Descripción
Sumario:Let d(N) (resp., p(N)) be the number of summands in the determinant (resp., permanent) of an N × 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 proving 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.