Algebraic and combinatorial structures on pairs of twin binary trees
By Samuele Giraudo. 2012
62 citations recorded by the source corpus.
Abstract We give a new construction of a Hopf algebra defined first by Reading (2005) [Rea05] 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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/6d7a878b17b743a9758551ff6c3634ed8b7a4148
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Citations in the corpus
- Cambrian Hopf Algebras (2014, methodology): “rees, they necessarily have opposite canopy (see Section1.1.6), meaning that can(T ) i= can(T ) ifor all i2[n 1]. The reciprocal statement for the constant signature ( n) is proved by S. Giraudo in [Gir12]. Proposition 42 ([Gir12]). Two binary trees are twin if and only if they have opposite canopy.”