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A160368
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Number of self-orthogonal Latin squares of order n.
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3
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OFFSET
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1,4
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COMMENTS
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A self-orthogonal Latin square is a Latin square orthogonal to its transpose and a SOLS L is idempotent if L(i,i)=i. The number of distinct SOLS of order n may be determined by multiplying the number of idempotent SOLS of order n by n!.
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REFERENCES
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G. P. Graham and C.E. Roberts, 2006. Enumeration and isomorphic classification of self-orthogonal Latin squares, Journal of Combinatorial Mathematics and Combinatorial Computing, 59, pp. 101-118.
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LINKS
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Table of n, a(n) for n=1..10.
A. P. Burger, M. P. Kidd and J. H. van Vuuren, 2010. Enumerasie van self-ortogonale Latynse vierkante van orde 10, LitNet Akademies (Natuurwetenskappe), 7(3), pp 1-22.
A. P. Burger, M. P. Kidd and J. H. van Vuuren, Enumeration of isomorphism classes of self-orthogonal Latin squares, Ars Combinatoria, 97, pp. 143-152.
M. P. Kidd, A repository of self-orthogonal Latin squares
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CROSSREFS
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Cf. A160365, A160366, n!*A160367.
Sequence in context: A174113 A089272 A004362 * A062195 A004386 A076003
Adjacent sequences: A160365 A160366 A160367 * A160369 A160370 A160371
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KEYWORD
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hard,more,nonn
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AUTHOR
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Martin P Kidd, May 11 2009
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EXTENSIONS
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References updated and a link updated by Martin P Kidd, Aug 14 2010
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STATUS
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approved
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