A160368 Number of self-orthogonal Latin squares of order n.

1, 0, 0, 48, 1440, 0, 19353600, 4180377600, 25070769561600, 3200285563453440000

Offset: 1

Author

Martin P Kidd, May 11 2009

Keywords

• hard
• more
• nonn

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.
• M. P. Kidd, A repository of self-orthogonal Latin squares

Crossrefs

Cf. A160365, A160366, n!*A160367.

Extensions

References updated and a link updated by Martin P Kidd, Aug 14 2010