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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 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,7`
	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 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 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	`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`