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Lattice of combinatorial Hopf algebras: binary trees with multiplicities

Abstract : In a first part, we formalize the construction of combinatorial Hopf algebras from plactic-like monoids using polynomial realizations. Thank to this construction we reveal a lattice structure on those combinatorial Hopf algebras. As an application, we construct a new combinatorial Hopf algebra on binary trees with multiplicities and use it to prove a hook length formula for those trees.
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https://hal.inria.fr/hal-01229688
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Submitted on : Tuesday, November 17, 2015 - 10:19:58 AM
Last modification on : Sunday, June 26, 2022 - 12:04:42 PM
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Jean-Baptiste Priez. Lattice of combinatorial Hopf algebras: binary trees with multiplicities. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.1137-1148, ⟨10.46298/dmtcs.2372⟩. ⟨hal-01229688⟩

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