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The algebraic combinatorics of snakes

Abstract : Snakes are analogues of alternating permutations defined for any Coxeter group. We study these objects from the point of view of combinatorial Hopf algebras, such as noncommutative symmetric functions and their generalizations. The main purpose is to show that several properties of the generating functions of snakes, such as differential equations or closed form as trigonometric functions, can be lifted at the level of noncommutative symmetric functions or free quasisymmetric functions. The results take the form of algebraic identities for type B noncommutative symmetric functions, noncommutative supersymmetric functions and colored free quasisymmetric functions.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00735009
Contributor : Matthieu Josuat-Vergès <>
Submitted on : Tuesday, September 25, 2012 - 10:07:46 AM
Last modification on : Wednesday, February 26, 2020 - 7:06:07 PM
Long-term archiving on: : Wednesday, December 26, 2012 - 4:10:11 AM

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Matthieu Josuat-Vergès, Jean-Christophe Novelli, Jean-Yves Thibon. The algebraic combinatorics of snakes. Journal of Combinatorial Theory, Series A, Elsevier, 2012, 119 (8), pp.1613-1638. ⟨10.1016/j.jcta.2012.05.002⟩. ⟨hal-00735009⟩

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