Combinatorics Seminar: The Hopf monoid of orbit polytopes and its character group

Seminar | October 22 | 12:10-1 p.m. | 939 Evans Hall

 Mariel Supina, UC Berkeley

 Department of Mathematics

A Hopf monoid is an algebraic structure that many families of combinatorial objects share. The collection of multiplicative functions defined on a Hopf monoid forms a group, called the character group. Aguiar and Ardila (2017) proved that the character groups for the Hopf monoids of permutahedra and associahedra are exponential power series under multiplication and composition, respectively. In this talk I will introduce the Hopf monoid of orbit polytopes, and then I will discuss some of my recent work on determining the structure of the character group of this Hopf monoid.