DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Co-organizers:

Andrew Baxter, Rutgers University, baxter{at} math [dot] rutgers [dot] edu

Lara Pudwell, Rutgers University, lpudwell {at} math [dot] rutgers [dot] edu

Doron Zeilberger, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Experimenting With Matroids

Speaker: Sandra Kingan, DIMACS

Date: Thursday, September 27, 2007 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

In this talk I will describe Oid, a software system for experimenting with matroids. Several combinatorial objects such as graphs, matrices, linear spaces, and lattices can be viewed as matroids. Oid accepts matroids in different formats and can check them for isomorphism. It can list the bases, circuits, flats, connectivity function, Tutte polynomial, etc. For matroids represented as matrices, it has a finite field engine that handles structural computations such as deletions, contractions, extensions, and coextensions. Code from Oid's library can be used to make stand-alone programs for computing splitters, stabilizers, and minimal excluded minors. I will describe how we use Oid to automate case analyses in structural results. We also use Oid to generate data and discover patterns that lead to conjectures, which we then prove by completely theoretical methods.