Mixed Volume of Matroids

Matroids are combinatorial objects that abstract the notion of independence. Given any matroid, Feichtner and Yuzvinsky defined a graded commutative ring called the Chow ring, inspired by algebraic geometry. To each matroid, we can define a linear map called the mixed volume of the matroid, which completely determines the Chow ring. In a recent work by Braden, Huh, Matherne, Proudfoot, and Wang, they provide a decomposition of the Chow ring by decomposing the matroid using the deletion operation. Following a similar method, we give an inductive formula for computing the mixed volume of a matroid. This is joint work with Kalle Karu and Jonathan Yang.