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A160365
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Number of (row,column)-paratopism classes of self-orthogonal Latin squares of order n.
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3
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OFFSET
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1,7
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COMMENTS
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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.
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REFERENCES
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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.
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LINKS
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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
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CROSSREFS
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Cf. A160366, A160367, A160368.
Sequence in context: A213142 A357540 A097572 * A264517 A080509 A063439
Adjacent sequences: A160362 A160363 A160364 * A160366 A160367 A160368
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KEYWORD
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hard,more,nonn
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AUTHOR
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Martin P Kidd, May 11 2009
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EXTENSIONS
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Class names corrected by, References updated by, Link updated by Martin P Kidd, Aug 14 2010
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STATUS
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approved
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