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SUMMARY:Large transversals in Equi-n-squares - Richard Montgomery (Warwick
 )
DTSTART:20241205T143000Z
DTEND:20241205T153000Z
UID:TALK225394@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION: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 i
 s\, he conjectured that every equi-n-square must contain a transversal wit
 h n-1 cells. If true\, this would be a widespread generalisation of the we
 ll-known Ryser-Brualdi-Stein conjecture on Latin squares\, but\, as shown 
 by Pokrovskiy and Sudakov in 2019\, Stein's equi-n-square conjecture is fa
 lse. 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
 .\n\nThis is joint work with Debsoumya Chakraborti and Teo Petrov.
LOCATION:MR12
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