skip to content
 

On polynomials arising from zonotopal algebra

Date: 
Wednesday 23rd January 2008 - 15:30 to 16:00
Venue: 
INI Seminar Room 1
Abstract: 

Given a graph G, we consider its associated (linear) matroid X, and associate X with three kinds of algebraic structures called external, central, and internal. Each algebraic structure is given in terms of a pair of homogeneous polynomial ideals in n variables that are dual to each other. Algebraically, one encodes properties of the (generic) hyperplane arrangement H(X) associated to X, while the other encodes by duality the properties of the zonotope Z(X) built from the matrix X. These algebraic structures are then applied to obtain various statistics for the graph G. In particular, the Hilbert series of each of the three ideals turn out to be ultimately related to the Tutte polynomial of G, and the grading of the ideals turns out to be related to specific counting functions on subforests or on spanning trees of G. This leads to other combinatorial connections and several open problems as well.

Related Links

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons