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A160368
Number of self-orthogonal Latin squares of order n.
10
1, 0, 0, 48, 1440, 0, 19353600, 4180377600, 25070769561600, 3200285563453440000
OFFSET
1,4
COMMENTS
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!.
REFERENCES
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.
LINKS
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.
CROSSREFS
Sequence in context: A174113 A089272 A004362 * A275042 A062195 A264322
KEYWORD
hard,more,nonn
AUTHOR
Martin P Kidd, May 11 2009
EXTENSIONS
References updated and a link updated by Martin P Kidd, Aug 14 2010
STATUS
approved