

A160365


Number of (row,column)paratopism classes of selforthogonal Latin squares of order n.


3




OFFSET

1,7


COMMENTS

A selforthogonal 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 selforthogonal Latin squares was performed via an (almost) exhaustive computerised 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 selforthogonal Latin squares, Journal of Combinatorial Mathematics and Combinatorial Computing, 59, pp. 101118.


LINKS

Table of n, a(n) for n=1..10.
A. P. Burger, M. P. Kidd and J. H. van Vuuren, 2010. Enumerasie van selfortogonale Latynse vierkante van orde 10, LitNet Akademies (Natuurwetenskappe), 7(3), pp 122.
A. P. Burger, M. P. Kidd and J. H. van Vuuren, Enumeration of isomorphism classes of selforthogonal Latin squares, Ars Combinatoria, 97, pp. 143152.
M. P. Kidd, A repository of selforthogonal Latin squares


CROSSREFS

Cf. A160366, A160367, A160368.
Sequence in context: A213142 A357540 A097572 * A264517 A080509 A063439
Adjacent sequences: A160362 A160363 A160364 * A160366 A160367 A160368


KEYWORD

hard,more,nonn


AUTHOR

Martin P Kidd, May 11 2009


EXTENSIONS

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


STATUS

approved



