Mathematical Sciences Department
Discrete Math Seminar
Speaker: Ralihe Raul Villagran, WPI
Monday, September 25, 2023
3:00 pm – 3:50 pm
Unity Hall 405
Title: Determinantal ideals and sandpile groups of graphs
Abstract: Given a graph G=(V,E) with Laplacian matrix L(G) = Deg(G) - A(G). Then the algebraic structure of the sandpile group of G. denoted as S(G), can be described by (the Smith normal form of) its Laplacian matrix. In this talk we introduce the generalized Laplacian matrix (of G), L(G,X) = Diag(X)-A(G) and its determinantal ideals (the ideals generated by the determinants of submatrices of certain size). Moreover, we will see some examples on how these ideals can be helpful in the study of sandpile groups.