Commutative Hopf algebras of permutations and trees

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We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures, and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general construction based on graphs, and its non-commutative dual is realized in three different ways, in particular as the Grossman-Larson algebra of heap ordered trees. Extensions to endofunctions, parking functions, set partitions, planar binary trees and rooted forests are discussed. Finally, we introduce one-parameter families interpolating between different structures constructed on the same combinatorial objects.
18 pages, LaTEX

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Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/74274

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0502456
 http://arxiv.org/abs/math/0502456

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arXiv