Algebraic and combinatorial structures on Baxter permutations

Details Algebraic and combinatorial structures on Baxter permutations Algebraic and combinatorial structures on Baxter permutations

2010-11-18

arxiv.org/abs/1011.4288v3

Formal Power Series and Algebraic Combinatorics, 387--398, 2011

Mathematics

Combinatorics

12 pages. This is the proceedings conference version. The full-length journal version is arXiv:1204.4776v1

Scientific paper

We give a new construction of a Hopf subalgebra of the Hopf algebra of Free quasi-symmetric functions whose bases are indexed by objects belonging to the Baxter combinatorial family (i.e. Baxter permutations, pairs of twin binary trees, etc.). This construction relies on the definition of the Baxter monoid, analog of the plactic monoid and the sylvester monoid, and on a Robinson-Schensted-like insertion algorithm. The algebraic properties of this Hopf algebra are studied. This Hopf algebra appeared for the first time in the work of Reading [Lattice congruences, fans and Hopf algebras, Journal of Combinatorial Theory Series A, 110:237--273, 2005].

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