A160367 Number of idempotent self-orthogonal Latin squares of order n.

1, 0, 0, 2, 12, 0, 3840, 103680, 69088320, 881912908800

Offset

1,4

Comments

A self-orthogonal Latin square (SOLS) is a Latin square orthogonal to its transpose and a SOLS L is idempotent if L(i,i)=i. Two SOLS L and L' are (row,column)-paratopic if a permutation p applied to the rows and columns of L and a permutation q applied to the symbol set of L transforms L into L', in which case (p,q) is an (row,column)-paratopism from L to L'. An (row,column)-autoparatopism is an (row,column)-paratopism that maps L to itself. The number of idempotent SOLS of order n may be found by the formula sum_{L in I(n)}2n!/|A(L)|, where I(n) is a set of (row,column)-paratopism class representatives of SOLS of order n and A(L) is the (row,column)-autoparatopism group of L. A set of (row,column)-paratopism class representatives may be found at www.vuuren.co.za -> Repositories.

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

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

Crossrefs

A160365, A160366, A160368

Sequence in context: A350258 A364781 A166489 * A016736 A287704 A351456

Adjacent sequences: A160364 A160365 A160366 * A160368 A160369 A160370

Keyword

hard,more,nonn

Author

Martin P Kidd, May 11 2009

Extensions

Class names corrected, references updated, and a link updated by Martin P Kidd, Aug 14 2010

Status

approved