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)|
|Number of pages||36|
|Journal||Australasian Journal of Combinatorics|
|State||Published - Jan 1 2018|
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics