Algebraic and combinatorial structures on pairs of twin binary trees

Details Algebraic and combinatorial structures on pairs of twin binary trees Algebraic and combinatorial structures on pairs of twin binary trees

2012-04-21

arxiv.org/abs/1204.4776v1

Journal of Algebra, 360, 115--157, 2012

Mathematics

Combinatorics

43 pages. arXiv admin note: substantial text overlap with arXiv:1011.4288

Scientific paper

10.1016/j.jalgebra.2012.03.020

We give a new construction of a Hopf algebra defined first by Reading whose bases are indexed by objects belonging to the Baxter combinatorial family (i.e., Baxter permutations, pairs of twin binary trees, etc.). Our construction relies on the definition of the Baxter monoid, analog of the plactic monoid and the sylvester monoid, and on a Robinson-Schensted-like correspondence and insertion algorithm. Indeed, the Baxter monoid leads to the definition of a lattice structure over pairs of twin binary trees and the definition of a Hopf algebra. The algebraic properties of this Hopf algebra are studied and among other, multiplicative bases are provided, and freeness and self-duality proved.

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