## Seminar:

Fall 2011, Thursdays, Milner 216, 4:00-4:50 PM
__ Date:__ ** October 20 **

**" Hyperpfaffians and their uses in Combinatorics "**

**Daniel Redelmeier**

__Abstract__In this talk we will discuss the hyperpfaffian, which is an extension of the pfaffian, which is in turn a generalisation of the determinant. We will spend the first part of the talk examining the different definitions used for the hyperpfaffian, as there are several non-equivalent forms. Then we will examine uses of the hyperpfaffian in combinatorics. The first is the Hyperpfaffian-Cactus theorem, which is related to the classical matrix-tree theorem and the later pfaffian-tree theorem. Second we will look at hyperpfaffian orientations, which can be used to count perfect matchings on a hypergraph. If time permits we will look at hyperpfaffian rings/ideals, and specifically look at the fact that unlike the pfaffian ideal, the hyperpfaffian ideal is not an algebra with straightening law (under reasonable assumptions).