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A091323
Minimum number of transversals in a Latin square of order 2n+1.
5
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)<=1721, a(6)<=43093, a(7)<=215721. - Eduard I. Vatutin, Apr 09 2024
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.
CROSSREFS
Sequence in context: A135584 A174538 A340821 * A174641 A217671 A118539
KEYWORD
nonn,hard,more
AUTHOR
Richard Bean, Feb 17 2004
EXTENSIONS
a(4) from Brendan McKay and Ian Wanless, May 23 2004
STATUS
approved