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

1, 3, 3, 3, 68

Offset

0,2

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

a(7)<=170369. - Dennis Yurichev, Sep 30 2025

References

H. J. Ryser, Neuere Probleme der Kombinatorik. Vorträge über Kombinatorik, Oberwolfach, 1967, Mathematisches Forschungsinstitut Oberwolfach, pp. 69-91.

Links

Table of n, a(n) for n=0..4.

Brendan D. McKay, Jeanette C. McLeod and Ian M. Wanless, The number of transversals in a Latin square, Des. Codes Cryptogr., 40, (2006) 269-284.

Vladimir N. Potapov, On the number of transversals in Latin squares, arxiv:1506.01577 [math.CO], 2015.

Eduard I. Vatutin, Proving list (best known examples).

Dennis Yurichev, L15 with 170369 transversals.

Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A090741, A092237.

Sequence in context: A135584 A174538 A340821 * A174641 A217671 A118539

Adjacent sequences: A091320 A091321 A091322 * A091324 A091325 A091326

Keyword

nonn,hard,more

Author

Richard Bean, Feb 17 2004

Extensions

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

Status

approved