The University of Michigan Combinatorics Seminar
Fall 2006
October 27, 4:10-5:00, 3866 East Hall



The Hopf algebra of posets

T. Kyle Petersen

University of Michigan


Abstract

Work of Aguiar, Bergeron, and Sottile established the category of "combinatorial Hopf algebras" and showed that the quasisymmetric functions are the terminal object in this category. Stembridge's peak functions form a special Hopf subalgebra of the quasisymmetric functions called the "odd" subalgebra; moreover, the algebra of peak functions is terminal in the category of odd combinatorial Hopf algebras.
We will survey this theory and show how these two important algebras can be easily understood in terms of another combinatorial Hopf algebra: the algebra of (equivalences classes of finite, labeled) posets. This talk is based on work joint with Sam Hsiao.