Algebra e Geometria allo SBAI
Aula 1B1, RM002
Jack Allsop (Monash University, Australia)
Latin squares without proper subsquares
(nel sito del dip. è presente la versione con apici e pedici corretti)
A Latin square of order n is an n × n matrix of n symbols, such that each symbol occurs exactly once in each row and column. A subsquare of order k is a k × k submatrix of a Latin square that is itself a Latin square. Every Latin square of order n contains n2 subsquares of order one, and one subsquare of order n. All other subsquares are called proper. If a Latin square contains no proper subsquares then it is called N∞ . Around 50 years ago Hilton conjectured that an N∞ Latin square of order n exists for all sufficiently large n. Hilton’s conjecture was previously known to hold for all integers n not of the form 2a 3b for integers a ≥ 1 and b ≥ 0. We resolve Hilton’s conjecture by constructing N∞ Latin squares for the remaining orders.