BIRS Workshop Lecture Videos
Counting weighted zero-sum sequences with the polynomial method Schmitt, John
The Erdos-Ginzburg-Ziv (EGZ) Theorem has an elegant proof due to Bailey and Richter that employs a 1935 result of Chevalley.Â 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.Â 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.Â 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.Â 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. Â Joint work with Pete L. Clark and Aden Forrow.
Item Citations and Data
Attribution-NonCommercial-NoDerivatives 4.0 International