Jean-Baptiste Priez - Lattice of combinatorial Hopf algebras: binary trees with multiplicities

dmtcs:2372 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2372
Lattice of combinatorial Hopf algebras: binary trees with multiplicitiesArticle

Authors: Jean-Baptiste Priez 1

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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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: hook length formula,polynomial realization,monoids,Combinatorial Hopf algebras,generating series,binary trees,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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