TAU Combinatorics Seminar 2020/21

When: Sunday, November 1, 10am
Speaker: Eden Kuperwasser, Tel Aviv University
Title: A sharp threshold for Schur's theorem in the integers modulo a prime


Following Schur's theorem we say that a subset $A$ of $Z_n$ is $r$-Schur if every $r$-coloring of the elements of $A$ admits three distinct elements $x$,$y$, and $z$ satisfying $x+y=z$ and all sharing the same color. We establish the existence of a sharp threshold for this property in random subsets of $Z_n$ where $n$ goes over the prime numbers, for any fixed number of colors $r$. The proof relies on Friedgut's criterion for sharp thresholds and the Container Lemma of Saxton and Thomason, and of Balogh, Morris, and Samotij.

Joint work with Wojciech Samotij.