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A090741
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Maximum number of transversals in a Latin square of order n.
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2
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OFFSET
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1,3
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COMMENTS
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a(10) >= 5504 from Parker.
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REFERENCES
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D. Bedford, Transversals in the Cayley tables of the non-cyclic groups of order 8, European Journal of Combinatorics, volume 12 (1991), 455-458.
N. J. Cavenagh and I. M. Wanless, On the number of transversals in Cayley tables of cyclic groups, Disc. Appl. Math. 158 (2010), 136-146.
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.
E. T. Parker, Computer investigations of orthogonal Latin squares of order 10, Proc. Sympos. Appl. Math., volume 15 (1963), 73-81.
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LINKS
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Table of n, a(n) for n=1..9.
Ian M. Wanless, A Generalization of Transversals for Latin Squares, Electronic Journal of Combinatorics, volume 9, number 1 (2002), R12.
Index entries for sequences related to Latin squares and rectangles
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FORMULA
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a(n) is asymptotically in between 3.2^n and 0.62^n n!. [McKay, McLeod, Wanless], [Cavenagh, Wanless] - From Ian Wanless, Jul 30 2010
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EXAMPLE
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a(1), a(3), a(5), a(7) are from the group tables for Z_1, Z_3, Z_5 and Z_7 (see sequence A006717); a(4) and a(8) are from Z_2 x Z_2 and the non-cyclic groups of order 8 (see Bedford).
a(9) = 2241 from Z_3 x Z_3.
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CROSSREFS
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Cf. A006717, A091325.
Sequence in context: A135350 A068038 A196087 * A032234 A032255 A137475
Adjacent sequences: A090738 A090739 A090740 * A090742 A090743 A090744
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KEYWORD
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hard,nonn
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AUTHOR
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Richard Bean (rwb(AT)eskimo.com), Feb 03 2004
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EXTENSIONS
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a(9) = 2241 from Brendan McKay and Ian Wanless, May 23, 2004
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STATUS
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approved
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