# Combinatorics Seminar- The Free Cone and its relation to matroid invariants

Speaker: Kevin Long, GWU
Date and time: Thursday, November 14, 2:15–3:15pm
Place: Phillips 110
Title: The Free Cone and its relation to matroid invariants
Abstract: The G-invariant is a matroid invariant that determines the Tutte polynomial, and is of particular interest due to its universality among valuative invariants of matroids. Given a matroid M, we define a new matroid construction called the free cone of M, and prove that its G-invariant is determined by the G-invariant of M. We also look at the configuration, a matroid invariant that determines the G-invariant, and prove that the configuration of M determines the free cone of M.