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

%I A160365 #14 Jul 11 2025 18:39:54
%S A160365 1,0,0,1,1,0,4,4,175,121642
%N A160365 Number of (row,column)-paratopism classes of self-orthogonal Latin squares of order n.
%C A160365 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.
%D A160365 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.
%H A160365 A. P. Burger, M. P. Kidd and J. H. van Vuuren, 2010. <a href="http://www.vuuren.co.za/papers/SOLSEnum10.pdf">Enumerasie van self-ortogonale Latynse vierkante van orde 10</a>, LitNet Akademies (Natuurwetenskappe), 7(3), pp 1-22.
%H A160365 A. P. Burger, M. P. Kidd and J. H. van Vuuren, <a href="http://www.vuuren.co.za/papers/SOLSEnum.pdf">Enumeration of isomorphism classes of self-orthogonal Latin squares</a>, Ars Combinatoria, 97, pp. 143-152.
%H A160365 M. P. Kidd, <a href="http://www.vuuren.co.za/main.php">A repository of self-orthogonal Latin squares</a>
%Y A160365 Cf. A160366, A160367, A160368.
%K A160365 hard,more,nonn
%O A160365 1,7
%A A160365 _Martin P Kidd_, May 11 2009
%E A160365 Class names corrected by, References updated by, Link updated by _Martin P Kidd_, Aug 14 2010