Some combinatorial Hopf algebras
Abstract: We will discuss several "combinatorial" Hopf algebras, with close connections to Stanley's theory of poset partitions and quasi-symmetric functions.
The structure of these Hopf algebras is intimately related to certain partial orders which are recurrent in combinatorics, like the weak Bruhat order on permutations and the Tamari order on binary trees.
Little background in either Hopf algebras or combinatorics will be assumed, though some familiarity would be helpful. No technical results will be presented. The goal will be to present an overview which may be useful to professors and students with related interests.