On the Ryser-Brualdi-Stein conjecture

Abstract: The Ryser-Brualdi-Stein conjecture states that every Latin square of order $n$ should have a partial transversal with $n-1$ elements, and a full transversal if $n$ is odd. In 2020, Keevash, Pokrovskiy, Sudakov and Yepremyan improved the long-standing best known bounds on this conjecture by showing that a partial transversal with $n-O(\log n/\log\log n)$ elements always exists. I will discuss how to show, for large $n$, that a partial transversal with $n-1$ elements always exists.

combinatorics

Audience: researchers in the topic

Warwick Combinatorics Seminar

Series comments: This is the online combinatorics seminar at Warwick.