Open Collections

Counting weighted zero-sum sequences with the polynomial method

Banff International Research Station for Mathematical Innovation and Discovery

The Erdos-Ginzburg-Ziv (EGZ) Theorem has an elegant proof due to Bailey and Richter that employs a 1935 result of Chevalley.  Chevalleyâ s Theorem states that the number of shared zeros of a polynomial system over a finite field is not equal to one whenever the number of variables exceeds the sum of the degrees of the polynomials.  In the same year, Warning generalized Chevalleyâ s Theorem and gave a lower bound on the number of shared zeros in such a system so long as one exists.  We discuss our generalization of Warningâ s Theorem and show how we can quantitatively refine existence theorems, such as EGZ, and simultaneously include the inhomogeneous case.  Specifically, we show how one can apply our theorem to recover a 2012 result of Das Adhikari, Grynkiewicz and Sun that treats an analogue of the EGZ Theorem, one in which one considers the EGZ-problem for generalized zero-sum subsequences in any finite commutative p-group.   Joint work with Pete L. Clark and Aden Forrow.

Mathematics; Combinatorics; Number theory; Discrete mathematics

video/mp4

Author affiliation: Middlebury College

2020-05-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/74385

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/