University of Birmingham > Talks@bham > Combinatorics and Probability Seminar > Ryser's conjecture and more

## Ryser's conjecture and moreAdd to your list(s) Download to your calendar using vCal - Liana Yepremyan (University of Illinois at Chicago)
- Thursday 15 October 2020, 16:00-17:00
- https://bham-ac-uk.zoom.us/j/83022685017?pwd=L1RQclI2dmIvL2RXeUNCblpuanlBUT09.
If you have a question about this talk, please contact M.Jenssen. A Latin square of order $n$ is an $n \times n$ array filled with $n$ symbols such that each symbol appears only once in every row or column and a transversal is a collection of cells which do not share the same row, column or symbol. The study of Latin squares goes back more than 200 years to the work of Euler. One of the most famous open problems in this area is a conjecture of Ryser, Brualdi and Stein from 60s which says that every Latin square of order $n\times n$ contains a transversal of order $n-1$. A closely related problem is 40 year old conjecture of Brouwer that every Steiner triple system of order $n$ contains a matching of size $(n-4)/3$. The third problem we’d like to mention asks how many distinct symbols in Latin arrays suffice to guarantee a full transversal? In this talk we discuss a novel approach to attack these problems.
Joint work with Peter Keevash, Alexey Pokrovskiy and Benny Sudakov.
Meeting ID: 830 2268 5017 Passcode: 101833 This talk is part of the Combinatorics and Probability Seminar series. ## This talk is included in these lists:- Combinatorics and Probability Seminar
- School of Mathematics Events
- https://bham-ac-uk.zoom.us/j/83022685017?pwd=L1RQclI2dmIvL2RXeUNCblpuanlBUT09
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