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...
| Autores: | , , , |
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| 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 |
| 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. |
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