Geometry Seminar
Hypergaph and Fractional Generalizations of the Erdős-Ginzburg-Ziv Theorem
Speaker: Steve Simon, Bard College
Location: Warren Weaver Hall 1314
Date:
Tuesday, April 30, 2024, 6 p.m. CANCELLED
Synopsis:
A cornerstone result of Erdős, Ginzburg, and Ziv (EGZ) states that any sequence of \(2n-1\) elements in \(\mathbb{Z}/n\) contains a zero-sum subsequence of length \(n\). While algebraic techniques have predominated in deriving many deep generalizations of this theorem over the past sixty years, here we introduce topological approaches to zero-sum problems which have proven fruitful in other combinatorial contexts. Our main result is a topological criterion for determining when any \(\mathbb{Z}/n\)-coloring ing of an -uniform hypergraph contains a zero-sum hyperedge. In addition to applications for Kneser hypergraphs, for complete hypergraphs our methods recover Olson's generalization of the EGZ theorem for arbitrary finite groups.
In addition, we give a fractional generalization of the EGZ theorem with applications to balanced set families.
Notes:
April 30 seminar has been cancelled due to circumstances outside our control.