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arXiv · 1511.00426

Number of right ideals and a $q$-analogue of indecomposable permutations

Roland Bacher·Christophe Reutenauer
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Abstract

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 $(q-1)^{n+1} q^{\frac{(n+1)(n-2)}{2}}\sum\_θq^{inv(θ)}$, where the sum is over all indecomposable permutations in $S\_{n+1}$ and where $inv(θ)$stands for the number of inversions of $θ$.

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Roland Bacher, Christophe Reutenauer. 2015-11-02. Number of right ideals and a $q$-analogue of indecomposable permutations. https://arxiv.org/abs/1511.00426

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