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Lattice of combinatorial Hopf algebras: binary trees with multiplicities. (English) Zbl 1294.05191
Proceedings of the 25th international conference on formal power series and algebraic combinatorics, FPSAC 2013, Paris, France, June 24–28, 2013. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Mathematics and Theoretical Computer Science. Proceedings, 1137-1148, electronic only (2013).
Summary: 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.
For the entire collection see [Zbl 1281.05001].

MSC:
05E15 Combinatorial aspects of groups and algebras (MSC2010)
05C05 Trees
16T05 Hopf algebras and their applications
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