Geodesic
Structure coefficients of the Hecke algebra of $(\mathcal{S}_{2n}, \mathcal{B}_n)$
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013).

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The Hecke algebra of the pair $(\mathcal{S}_{2n}, \mathcal{B}_n)$, where $\mathcal{B}_n$ is the hyperoctahedral subgroup of $\mathcal{S}_{2n}$, was introduced by James in 1961. It is a natural analogue of the center of the symmetric group algebra. In this paper, we give a polynomiality property of its structure coefficients. Our main tool is a combinatorial universal algebra which projects on the Hecke algebra of $(\mathcal{S}_{2n}, \mathcal{B}_n)$ for every $n$. To build it, we introduce new objects called partial bijections. 
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     author = {Tout, Omar},
     title = {Structure coefficients of the {Hecke} algebra of $(\mathcal{S}_{2n}, \mathcal{B}_n)$},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
     year = {2013},
     doi = {10.46298/dmtcs.2323},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2323/}
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Tout, Omar. Structure coefficients of the Hecke algebra of $(\mathcal{S}_{2n}, \mathcal{B}_n)$. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013). doi : 10.46298/dmtcs.2323. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2323/

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