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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
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:19:58 AM
Last modification on : Saturday, May 1, 2021 - 3:40:03 AM
Long-term archiving on: : Thursday, February 18, 2016 - 11:38:51 AM

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  • HAL Id : hal-01229688, version 1

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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. ⟨hal-01229688⟩

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