Geodesic
Lattice of combinatorial Hopf algebras: binary trees with multiplicities
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013).

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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. 
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     author = {Priez, Jean-Baptiste},
     title = {Lattice of combinatorial {Hopf} algebras: binary trees with multiplicities},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
     year = {2013},
     doi = {10.46298/dmtcs.2372},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2372/}
}
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Priez, Jean-Baptiste. Lattice of combinatorial Hopf algebras: binary trees with multiplicities. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013). doi : 10.46298/dmtcs.2372. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2372/

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