REVIEW 1 cited by
Almost every Latin square has a decomposition into transversals
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
In 1782, Euler conjectured that no Latin square of order $n\equiv 2\; \textrm{mod}\; 4$ has a decomposition into transversals. While confirmed for $n=6$ by Tarry in 1900, Bose, Parker, and Shrikhande constructed counterexamples in 1960 for each $n\equiv 2\; \textrm{mod}\; 4$ with $n\geq 10$. We show that, in fact, counterexamples are extremely common, by showing that if a Latin square of order $n$ is chosen uniformly at random then with high probability it has a decomposition into transversals.
Forward citations
Cited by 1 Pith paper
-
Latin Squares whose transversals intersect in unusual ways
Latin squares of all even orders >= 28 except 30 are constructed so that every two transversals meet while no entry lies in all transversals (proved for orders up to 10,000); dominant transversals exist for all orders...
Discussion (0). Continue with ORCID to comment.