Monomial bases related to the n! conjecture
AVAL, Jean-Christophe
Théorie des Nombres et Algorithmique Arithmétique [A2X]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Théorie des Nombres et Algorithmique Arithmétique [A2X]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
AVAL, Jean-Christophe
Théorie des Nombres et Algorithmique Arithmétique [A2X]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
< Réduire
Théorie des Nombres et Algorithmique Arithmétique [A2X]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Langue
en
Article de revue
Ce document a été publié dans
Discrete Mathematics. 2000, vol. 224, p. 15-35
Elsevier
Résumé en anglais
The purpose of this paper is to find a new way to prove the $n!$ conjecture for particular partitions. The idea is to construct a monomial and explicit basis for the space $M_{\mu}$. We succeed completely for hook-shaped ...Lire la suite >
The purpose of this paper is to find a new way to prove the $n!$ conjecture for particular partitions. The idea is to construct a monomial and explicit basis for the space $M_{\mu}$. We succeed completely for hook-shaped partitions, i.e., $\mu=(K+1,1^L)$. We are able to exhibit a basis and to verify that its cardinality is indeed $n!$, that it is linearly independent and that it spans $M_{\mu}$. We derive from this study an explicit and simple basis for $I_{\mu}$, the annihilator ideal of $\Delta_{\mu}$. This method is also successful for giving directly a basis for the homogeneous subspace of $M_{\mu}$ consisting of elements of $0$ $x$-degree.< Réduire
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