DMS Combinatorics Seminar

Speaker: Zach Walsh, Auburn University

Title: Delta-modular matroids

Abstract: An integer matrix is totally \(D\)-modular if the absolute value of the determinant of every square submatrix is at most \(D\). How many distinct columns can a rank-\(r\) totally \(D\)-modular matrix have? We will show how recent progress was made on this question via matroids, which are discrete structures that provide a combinatorial abstraction of linear independence.

This is joint work with Joseph Paat, Into Stallknecht, and Luze Xu.