Bases explicites et conjecture n!

Details Bases explicites et conjecture n! Bases explicites et conjecture n!

2007-11-06

arxiv.org/abs/0711.0899v1

Dans Formal Power Series and Algebraic Combinatorics - Formal Power Series and Algebraic Combinatorics, Moscou : Russie (1999)

Mathematics

Combinatorics

Scientific paper

The aim of this work is to construct a monomial and explicit basis for the space $M_{\mu}$ relative to the $n!$ conjecture. We succeed completely for hook-shaped partitions, i.e. $\mu=(K+1,1^L)$. We are indeed able to exhibit a basis and to verify that its cardinality is $n!$, that it is linearly independent and that it spans $M_{\mu}$. We deduce from this study an explicit and simple basis for $I_{\mu}$, the annulator 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.

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