Combinatorics Seminar: Mobius Inversion as Duality for Hopf Monoids

Seminar | March 11 | 12:10-1 p.m. | 939 Evans Hall

 Mario Sanchez, UC Berkeley

 Department of Mathematics

In this talk I will introduce an interesting connection between the theory of Hopf monoids in combinatorics and Mobius inversion. Roughly, a Hopf monoid is an algebraic abstraction of families of combinatorial objects which have an operation which combines objects and an operation which breaks objects apart. Like many algebraic structures, Hopf monoids have a nice notion of duality. We will show that for many combinatorial families, this notion of duality can be interpreted as Mobius inversion in an appropriate poset. We will focus on the examples of symmetric functions, graphs, and scheduling problems. No previous knowledge of Hopf monoids will be assumed.