A091323 Minimum number of transversals in a Latin square of order 2n+1.

1, 3, 3, 3, 68

Offset: 0

Author

Richard Bean, Feb 17 2004

Keywords

• nonn
• hard
• more

Comments

Ryser conjectured that a(n) >= 1 for all n. For even orders the number is 0, since the group table for Z_2n has no transversals.

a(5)<=814, a(6)<=43093, a(7)<=215721. - Eduard I. Vatutin, added Apr 09 2024, updated Jan 13 2025

References

• H. J. Ryser, Neuere Probleme der Kombinatorik. Vortraege ueber Kombinatorik, Oberwolfach, 1967, Mathematisches Forschungsinstitut Oberwolfach, pp. 69-91.

Links

• B. D. McKay, J. C. McLeod and I. M. Wanless, The number of transversals in a Latin square, Des. Codes Cryptogr., 40, (2006) 269-284.
• V. N. Potapov, On the number of transversals in Latin squares, arxiv:1506.01577 [math.CO], 2015.
• Eduard I. Vatutin, Proving list (best known examples).
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A090741, A092237.

Extensions

a(4) from Brendan McKay and Ian Wanless, May 23 2004