Abstract

Fuchs asked: For which integer partitions g1 +· · · gn = N does there exist a latin square of side N having n subsquares of sides g1, …,gn having no rows, columns, or symbols in common? Only when at most two distinct integer parts are used is the answer known completely; in general even the necessary conditions are elusive. Two conjectures giving plausible sufficient conditions are advanced. The first asserts than whenever the largest three integer parts are the same, such a latin square always exists. The second asserts that whenever the largest part is no larger than n − 2 times the smallest, such a latin square always exists. Partial results on both are established.

Original languageEnglish (US)
Pages (from-to)501-536
Number of pages36
JournalAustralasian Journal of Combinatorics
Volume71
Issue number3
StatePublished - Jan 1 2018

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Integer Partitions
Integer
Distinct
Partial
Necessary Conditions
Sufficient Conditions

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

On a latin square problem of fuchs. / Colbourn, Charles.

In: Australasian Journal of Combinatorics, Vol. 71, No. 3, 01.01.2018, p. 501-536.

Research output: Contribution to journalArticle

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