Geodesic
Number of Right Ideals and a q-analogue of Indecomposable Permutations
Canadian journal of mathematics, Tome 68 (2016) no. 3, pp. 481-503

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DOI

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 $${{\left( q-1 \right)}^{n+1}}_{{}}{{q}^{\frac{\left( n+1 \right)\left( n-2 \right)}{2}}}\sum\limits_{\theta }{{{q}^{inv\left( \theta\right)}}}$$ ,where the sum is over all indecomposable permutations in ${{S}_{n+1}}$ and where inv $\left( \theta \right)$ stands for the number of inversions of $\theta $ .
DOI : 10.4153/CJM-2016-004-8
Mots-clés : 05A15, 05A19, Keywords, permutation, indecomposable permutation, subgroups of free groups 
Bacher, Roland; Reutenauer, Christophe. Number of Right Ideals and a q-analogue of Indecomposable Permutations. Canadian journal of mathematics, Tome 68 (2016) no. 3, pp. 481-503. doi: 10.4153/CJM-2016-004-8
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     title = {Number of {Right} {Ideals} and a q-analogue of {Indecomposable} {Permutations}},
     journal = {Canadian journal of mathematics},
     pages = {481--503},
     year = {2016},
     volume = {68},
     number = {3},
     doi = {10.4153/CJM-2016-004-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-004-8/}
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