On the size of subsets of F_p^n without p distinct elements summing to zero

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• Lisa Sauermann (Stanford University)
• Wednesday 19 February 2020, 13:45-14:45
• MR4, CMS.

If you have a question about this talk, please contact Thomas Bloom.

Let us fix a prime p. The Erdös-Ginzburg-Ziv problem asks for the minimum integer s such that any collection of s points in the lattice Z^n contains p points whose centroid is also a lattice point in Z^n. For large n, this is essentially equivalent to asking for the maximum size of a subset of F_p^n without p distinct elements summing to zero.

In this talk, we discuss a new upper bound for this problem for any fixed prime p\geq 5 and large n. Our proof uses the so-called multi-colored sum-free theorem which is a consequence of the Croot-Lev-Pach polynomial method, as well as some new combinatorial ideas.

This talk is part of the Discrete Analysis Seminar series.

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