##### Department of Mathematics,

University of California San Diego

****************************

### Math 269 - Combinatorics

## Luca Moci

#### University of Rome \\ Department of Mathematics

## Tutte polynomial for toric arrangements

##### Abstract:

A toric arrangement is a finite family of hypersurfaces in a torus, every hypersurface being the kernel of a character. We describe some properties of such arrangements, by comparing them with hyperplane arrangements. The Tutte polinomial is an invariant which encodes a rich description of the topology and the combinatorics of a hyperplane arrangement, and satisfies a simple recurrence. We introduce the analogue of this polynomial for a toric arrangement. Furthermore, we show that our polynomial computes the volume of the related zonotope, counts its integral points, and provides the graded dimension of a space of quasipolynomials introduced by Dahmen and Micchelli to study partition functions.

Host: Jeff Remmel

### April 20, 2010

### 4:00 PM

### AP&M 7321

****************************