Large transversals in Equi-n-squares

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• Richard Montgomery (Warwick)
• Thursday 05 December 2024, 14:30-15:30
• MR12.

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In 1975 Stein conjectured that any n by n square in which each cell has one of n symbols, so that each symbol is used exactly n times, contains a set of n-1 cells which share no row, column or symbol. That is, he conjectured that every equi-n-square must contain a transversal with n-1 cells. If true, this would be a widespread generalisation of the well-known Ryser-Brualdi-Stein conjecture on Latin squares, but, as shown by Pokrovskiy and Sudakov in 2019, Stein’s equi-n-square conjecture is false. I will discuss the extent to which this conjecture is false, giving new bounds in both directions for the underlying extremal problem, and in particular show that an approximate version of Stein’s conjecture is true.

This is joint work with Debsoumya Chakraborti and Teo Petrov.

This talk is part of the Combinatorics Seminar series.

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