A160365 Number of (row,column)-paratopism classes of self-orthogonal Latin squares of order n.

1, 0, 0, 1, 1, 0, 4, 4, 175, 121642

Offset: 1

Author

Martin P Kidd, May 11 2009

Keywords

• hard
• more
• nonn

Comments

A self-orthogonal Latin square (SOLS) is a Latin square orthogonal to its transpose. Two SOLS L and L' are (row,column)-paratopic if two permutations, one applied to the rows and columns of L and one applied to the symbol set of L, transforms L into L'. Enumeration of the (row,column)-paratopism classes of self-orthogonal Latin squares was performed via an (almost) exhaustive computerized tree search. A number of pruning rules was used to eliminate (row,column)-paratopisms and generate one SOLS from each (row,column)-paratopism class (a repository of these class representatives may found at www.vuuren.co.za -> Repositories). As validation of the results two different approaches to the search tree was implemented.

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. A160366, A160367, A160368.

Extensions

Class names corrected by, References updated by, Link updated by Martin P Kidd, Aug 14 2010