Algebraic and combinatorial structures on Baxter permutations
نویسنده
چکیده
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]. Résumé. Nous proposons une nouvelle construction d’une sous-algèbre de Hopf de l’algèbre de Hopf des fonctions quasi-symétriques libres dont les bases sont indexées par les objets de la famille combinatoire de Baxter (i.e. permutations de Baxter, couples d’arbres binaires jumeaux, etc.). Cette construction repose sur la définition du monoı̈de de Baxter, analogue du monoı̈de plaxique et du monoı̈de sylvestre, et d’un algorithme d’insertion analogue à l’algorithme de Robinson-Schensted. Les propriétés algébriques de cette algèbre de Hopf sont étudiées. Cette algèbre de Hopf est apparue pour la première fois dans le travail de Reading [Lattice congruences, fans and Hopf algebras, Journal of Combinatorial Theory Series A, 110:237–273, 2005].
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Algebraic and combinatorial structures on pairs of twin binary trees
We give a new construction of a Hopf algebra defined first by Reading [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 RobinsonSchensted-like correspondence and insert...
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