Matroids over hyperfields

Series
Combinatorics Seminar
Time
Friday, March 11, 2016 - 3:05pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Matt Baker – School of Mathematics, Georgia Tech
Organizer
Esther Ezra
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.