Algebraic and combinatorial structures on pairs of twin binary trees
- 作者：Samuele Giraudo samuele.giraudo@univ-mlv.fr
- 关键词：Hopf algebra ; Robinson&ndash ; Schensted algorithm ; Quotient monoid ; Lattice ; Baxter permutation
- 刊名：Journal of Algebra
- 出版年：2012
- 期刊代码：69_00218693
- 类别：mt
- 出版时间：15 June, 2012
- 卷：360
- 期：Complete
- 页码：115-157
- 文件大小：671 K
摘要
We give a new construction of a Hopf algebra defined first by Reading (2005) 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.