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Sequence Subsums in Zero-Sum Theory

Banff International Research Station for Mathematical Innovation and Discovery

The last few years have seen the development and improvement of structural results in the area of sequence subsums over abelian groups. These results often have the flavor that either many elements can be represented as a sum of terms from  a subsequence of the given sequence (possibly with length restrictions) or else the sequence must itself be highly structured. The Subsum Kneser's Theorem, giving the corresponding analog of the classical Kneser's Theorem for sumsets,  is one such example. The statements of such results, particulary in their stronger forms, are often more challenging and technical in appearance, but they have been  utilized to strong effect when searching for zero-sums in a variety of  circumstances.   In this talk, we will give an overview of several of these results, focussing on how they were successfully used in various concrete extremal  problems involving zero-sums.

Mathematics; Combinatorics; Number theory; Discrete mathematics

video/mp4

Author affiliation: University of Memphis

2021-01-17

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/77124

Unreviewed

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