Algebraic and combinatorial structures on pairs of twin binary trees
Abstract
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 RobinsonSchenstedlike 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 selfduality proved.
 Publication:

arXiv eprints
 Pub Date:
 April 2012
 arXiv:
 arXiv:1204.4776
 Bibcode:
 2012arXiv1204.4776G
 Keywords:

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