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 language | English (US) |
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Pages (from-to) | 501-536 |
Number of pages | 36 |
Journal | Australasian Journal of Combinatorics |
Volume | 71 |
Issue number | 3 |
State | Published - Jan 1 2018 |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics