Number of right ideals and a $q$-analogue of indecomposable permutations
Résumé
We prove that the number of right ideals of codimension $n$ in
the algebra of noncommutative Laurent polynomials in two variables
over the finite field $\mathbb F_q$ is equal to
$(q-1)^{n+1} q^{\frac{(n+1)(n-2)}{2}}\sum_\theta q^{inv(\theta)}$, where the
sum is over all indecomposable permutations in $S_{n+1}$ and where $inv(\theta)$
stands for the number of inversions of $\theta$.
Domaines
Combinatoire [math.CO]
Origine : Fichiers produits par l'(les) auteur(s)
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