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University of Cambridge > Talks.cam > Discrete Analysis Seminar > On the size of subsets of F_p^n without p distinct elements summing to zero

## On the size of subsets of F_p^n without p distinct elements summing to zeroAdd to your list(s) Download to your calendar using vCal - 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 ErdÃ¶s-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. ## This talk is included in these lists:- All CMS events
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