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  1. Home > Articles & Issues >
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  3. Lattice of combinato ...
Conference paper

Lattice of combinatorial Hopf algebras: binary trees with multiplicities

Jean-Baptiste Priez (1)
(1) Laboratoire de Recherche en Informatique
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Imported on
November 21, 2016
Published on
December 31, 2012
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Proceedings
DOI
10.46298/dmtcs.2372
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https://about.hal.science/hal-authorisation-v1
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Lattice of combinatorial Hopf algebras: binary trees with multiplicities

Jean-Baptiste Priez (1)
(1) Laboratoire de Recherche en Informatique
Abstract
English
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.
French
Dans une première partie, nous formalisons la construction d’algèbres de Hopf combinatoires à partir d’une réalisation polynomiale et de monoïdes de type monoïde plaxique. Grâce à cette construction, nous mettons à jour une structure de treillis sur ces algèbres de Hopf combinatoires. Comme application, nous construisons une nouvelle algèbre de Hopf sur des arbres binaires à multiplicités et on l’utilise pour démontrer une formule des équerressur ces arbres.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • polynomial realization
  • hook length formula
  • generating series
  • binary trees
  • Combinatorial Hopf algebras
  • monoids
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