Matroids over rings

Algebra Seminar
Monday, March 25, 2013 - 15:05
1 hour (actually 50 minutes)
Skiles 005
N.C. State
Matroids are widely used objects in combinatorics; they arise naturally in many situations featuring vector configurations over a field.  But in some contexts the natural data are elements in a module over some other ring, and there is more than simply a matroid to be extracted.  In joint work with Luca Moci, we have defined the notion of matroid over a ring to fill this niche.  I will discuss two examples of situations producing these enriched objects, one relating to subtorus arrangements producing matroids over the integers, and one related to tropical geometry producing matroids over a valuation ring.  Time permitting, I'll also discuss the analogue of the Tutte invariant.