Geodesic
Commutative combinatorial Hopf algebras.
Journal of Algebraic Combinatorics, Tome 28 (2008) no. 1, pp. 65-95.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 noncommutative dual is realized in three different ways, in particular, as the Grossman-Larson algebra of heap-ordered trees. Extensions to endofunctions, parking functions, set compositions, 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.
Keywords: keywords Hopf algebras, quasi-symmetric functions, parking functions, trees, graphs 
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     title = {Commutative combinatorial {Hopf} algebras.},
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Hivert, Florent; Novelli, Jean-Christophe; Thibon, Jean-Yves. Commutative combinatorial Hopf algebras.. Journal of Algebraic Combinatorics, Tome 28 (2008) no. 1, pp. 65-95. http://geodesic.mathdoc.fr/item/JAC_2008__28_1_a7/