Mathematical Sciences Department Discrete Math Seminar: Ralihe Raul Villagran, WPI
Tuesday, December 10, 2024
3:00 pm to 3:50 pm
3:00 pm to 3:50 pm
Location
Floor/Room #
205
Title: On the structure of the sandpile group of threshold graphs and beyond
Abstract: In this talk, we will shortly review the algebraic and combinatorial structure of the sandpile groups for some graph families. In particular, we will review the description, given by Victor Reiner, Hans Christianson, and Brian Jacobson (about 20 years ago), on the sandpile group of threshold graphs. Then, inspired by the fact that the algebraic structure of the sandpile group of a graph is determined by the Smith normal form of its Laplacian matrix, we define the determinantal ideals of threshold graphs. Finally, we will present and try to answer some problems in this framework.
Audience(s)