Combinatorics Seminar

When: Sunday, Nov. 21, 10am Where: Schreiber 309 Speaker: Arie Bialostocki, University of Idaho Title: Recent Developments of the Erdos-Ginzburg-Ziv Theorem

Abstract:

In 1961 Erdos, Ginzburg and Ziv proved that among 2n-1 integers, we can always find n of them whose sum is divisible by n. In the last fifteen years a tremendous amount of results along the lines of the EGZ theorem, have been proved. In the introduction we will briefly address three philosophical questions: "what is a generalization of a theorem?", "what is a zero-sum theorem?" and "what is a generalization in the sense of a zero-sum theorem?" In the talk itself, first, we will survey some of the recent results (mostly unpublished yet) among them those by Reiher, Grynkiewicz and Elshholtz. Next, we will raise several open problems, among them multiplicity problems, the generalization in the sense of EGZ of the Alon Frankl Lovasz theorem and the Bialostocki Erdos Lefman problem. Finally, we will conclude with a discussion of possible developments of the weighted EGZ theorem conjectured by Caro.