Matroids over hyperfields

Combinatorics Seminar
Friday, March 11, 2016 - 15:05
1 hour (actually 50 minutes)
Skiles 005
School of Mathematics, Georgia Tech
We present an algebraic framework which simultaneously generalizes the notion of linear subspaces, matroids, valuated matroids, and oriented matroids. We call the resulting objects matroids over hyperfields. We give "cryptomorphic" axiom systems for such matroids in terms of circuits, Grassmann-Plucker functions, and dual pairs, and establish some basic duality theorems.