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Commutative combinatorial Hopf algebras

  • Florent Hivert
  • Jean-Christophe Novelli
  • Jean-Yves Thibon
Article

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 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

Hopf algebras Quasi-symmetric functions Parking functions Trees Graphs 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Florent Hivert
    • 1
  • Jean-Christophe Novelli
    • 1
  • Jean-Yves Thibon
    • 1
  1. 1.Laboratoire d’Informatique de l’Institut Gaspard MongeUniversité Paris-EstChamps-sur-MarneFrance

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