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Hopf algebra of permutation pattern functions

Abstract : We study permutation patterns from an algebraic combinatorics point of view. Using analogues of the classical shuffle and infiltration products for word, we define two new Hopf algebras of permutations related to the notion of permutation pattern. We show several remarkable properties of permutation patterns functions, as well their occurrence in other domains.
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Yannic Vargas. Hopf algebra of permutation pattern functions. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.839-850. ⟨hal-01207565⟩

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