Data evento: 
Giovedì, 28 Settembre, 2023 - 16:00

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 NLatin 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 NLatin squares for the remaining orders.

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