Commutative combinatorial Hopf algebras
Combinatorics
2013-02-12 v1
Abstract
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 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.
Cite
@article{arxiv.math/0605262,
title = {Commutative combinatorial Hopf algebras},
author = {F. Hivert and J. -C. Novelli and J. -Y. Thibon},
journal= {arXiv preprint arXiv:math/0605262},
year = {2013}
}
Comments
29 pages, LaTEX; expanded and updated version of math.CO/0502456