The Combinatorics Seminar meets on Wednesday, 3-4 PM, in Snow 408.
Please contact Jeremy Martin if you are interested in speaking.
Wednesday 2/27 Discussion: Chromatic Symmetric Functions, Hopf Algebras
Wednesday 3/6 No seminar
Wednesday 3/13 No seminar
Wednesday 3/20 No seminar (Spring Break)
Jeremy Martin Geometry of the Chip-Firing Game
Wednesday 4/3 No seminar
Wednesday 4/10 Discussion: Chromatic Symmetric Functions, Hopf Algebras
Smith Normal Form
Using Design Theory to Minimize Test Banks
Using Design Theory to Minimize Test Banks, II
Jacob White (Texas A&M)
Combinatorial Reciprocity and Hopf Rings in Combinatorics
Abstract: In this talk, we shall study ways to combine and decompose combinatorial objects, such as permutations, graphs, and set partitions. In more formal language, we will be studying examples of Hopf monoids in Joyal's category of species. These notions lead naturally to polynomial invariants for combinatorial objects, such as the chromatic polynomial of a graph, which come with nice interpretations when evaluated at -1. The interpretations involve the antipode of the Hopf monoid, which is a generalization of group inversion in algebra, and Mobius inversion in combinatorics. Determining the antipode of a Hopf monoid is a very challenging, combinatorial problem. We will discuss new approaches to the antipode problem via studying Hopf rings in species. The talk will cover work by Aguiar, Ardila, Mahajan, and myself.
Last updated Thu 5/2/13