Lauren Rose (Bard)

Module Bases for Integer Splines

Abstract for the Combinatorics Seminar
2019 March 5

Let G be a graph with n vertices and positive integer edge weights A. A vertex labeling (g1,...,gn) is an integer spline if for every pair of adjacent vertices {i,j} with edge weight a, gi = gj mod a. The set of splines on a given weighted graph (G,A) forms a free module of rank n over the integers. We provide an explicit construction for a particularly nice basis for this module, generalizing work done by undergraduates at Smith College and Bard College.

This is joint work with Jeff Suzuki and Jessica Liu.

To the Combinatorics Seminar Web page.