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Discrete Mathematics & Theoretical Computer Science |
Samuele Giraudo - Algebraic and combinatorial structures on Baxter permutations
dmtcs:2919 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2919Algebraic and combinatorial structures on Baxter permutationsArticle
Authors: Samuele Giraudo 
1
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 (\emphi.e. Baxter permutations, pairs of twin binary trees, \emphetc.). 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, \textitJournal of Combinatorial Theory Series A, 110:237–273, 2005].
Source: HAL:hal-00790742v2
Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: Hopf algebras,Robinson-Schensted algorithm,quotient monoid,Baxter permutations,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
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