====== 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 (g<sub>1</sub>,...,g<sub>n</sub>) is an //integer spline// if for every pair of adjacent vertices {i,j} with edge weight a, g<sub>i</sub> = g<sub>j</sub> 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.


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