Some Combinatorial Hopf Algebras

Marcelo Aguiar
Nantel Bergeron
Aaron Lauve
Frank Sottile
Abstract Here, we archive some MAPLE files we used in our general study of Combinatorial Hopf Algebras [ABS03], as well as our study of the Malvenuto-Reutenauer Hopf algebra [AS02] and of the Hopf algebra of planar binary trees [AS03]. This also contains numerous examples of the structure of these objects.

Table of Contents

  1. Algebra of Quasi-Symmetric Functions.
  2. Loday-Ronco Algebra of Planar Binary Trees.
  3. Malvenuto-Reutenauer Algebra of Permutations.
  4. Multiplihedra Module.

[ABS03] M. Aguiar, N. Bergeron, and F. Sottile, Combinatorial Hopf algebras and generalized Dehn-Sommerville relations, In preparation, 2003.
[AS02] M. Aguiar and F. Sottile, Structure of the Malvenuto-Reutenauer Hopf Algebra of Permutations, math.CO/0203282.
[AS03]                   , Structure of the Loday-Ronco Hopf Algebra of Planar Binary Trees, In preparation, 2003.

Work of Sottile supported by the National Science Foundation under grants DMS-0070494, CAREER DMS-0538734, and DMS-0701050.
Last Modified: 23 July 2008 by Frank Sottile