Jean-Baptiste Priez
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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)
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https://doi.org/10.46298/dmtcs.2372
Lattice of combinatorial Hopf algebras: binary trees with multiplicitiesConference paper
Authors: Jean-Baptiste Priez 1
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Jean-Baptiste Priez
1 Laboratoire de Recherche en Informatique
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.
Bin Bin Han;Wen Ting Zhang;Yan Feng Luo;Jin Xing Zhao, 2023, Representations and identities of hypoplactic monoids with involution, arXiv (Cornell University), 52, 3, pp. 1038-1062, 10.1080/00927872.2023.2255669, https://arxiv.org/abs/2301.12449.
Alan J. Cain;António Malheiro, 2018, Identities in Plactic, Hypoplactic, Sylvester, Baxter, and Related Monoids, The Electronic Journal of Combinatorics, 25, 3, 10.37236/6873, https://doi.org/10.37236/6873.