Combinatorics Seminar: Combinatorics of forward exchange matroids

Seminar | April 17 | 12:10-1 p.m. | 939 Evans Hall

 Bryan Gillespie, UC Berkeley

 Department of Mathematics

In this talk we will present several new results on forward exchange matroids, which are combinatorial structures that arise naturally in the theory of zonotopal algebra. In particular, a forward exchange matroid consists of an ordered matroid along with a choice of a certain type of order ideal on its bases. We will classify these objects by introducing an extension of Las Vergnas's external order on the bases of an ordered matroid. By identifying forward exchange matroids with order ideals in this extended ordering, we will derive an elegant recursive structure on these objects. This recursive structure may help to further unify the theory of the polynomial spaces constructed in zonotopal algebra.