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Algebraic properties for some permutation statistics
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) Cet article a éte moissonné depuis la source Episciences

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In this article, we study some quotient sets on permutations built from peaks, valleys, double rises and double descents. One part is dedicated to the enumeration of the cosets using the bijection of Francon-Viennot which is a bijection between permutations and the so-called Laguerre histories. Then we study the algebraic properties of these quotient sets. After having shown that some of them give rise to quotient algebras of $\mathbf{FQSym}$, we prove that they are also free. 
@article{DMTCS_2013_special_264_a29,
     author = {Vong, Vincent},
     title = {Algebraic properties for some permutation statistics},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2013},
     volume = {DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
     doi = {10.46298/dmtcs.2345},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2345/}
}
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Vong, Vincent. Algebraic properties for some permutation statistics. 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.2345

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