cp's OEIS Frontend

A160367 Number of idempotent self-orthogonal Latin squares of order n.

%I A160367 #8 Mar 31 2012 20:25:00
%S A160367 1,0,0,2,12,0,3840,103680,69088320,881912908800
%N A160367 Number of idempotent self-orthogonal Latin squares of order n.
%C A160367 A self-orthogonal Latin square (SOLS) is a Latin square orthogonal to its transpose and a SOLS L is idempotent if L(i,i)=i. Two SOLS L and L' are (row,column)-paratopic if a permutation p applied to the rows and columns of L and a permutation q applied to the symbol set of L transforms L into L', in which case (p,q) is an (row,column)-paratopism from L to L'. An (row,column)-autoparatopism is an (row,column)-paratopism that maps L to itself. The number of idempotent SOLS of order n may be found by the formula sum_{L in I(n)}2n!/|A(L)|, where I(n) is a set of (row,column)-paratopism class representatives of SOLS of order n and A(L) is the (row,column)-autoparatopism group of L. A set of (row,column)-paratopism class representatives may be found at www.vuuren.co.za -> Repositories.
%D A160367 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 A160367 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 A160367 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 A160367 M. P. Kidd, <a href="http://www.vuuren.co.za/main.php">A repository of self-orthogonal Latin squares</a>
%Y A160367 A160365, A160366, A160368
%K A160367 hard,more,nonn
%O A160367 1,4
%A A160367 _Martin P Kidd_, May 11 2009
%E A160367 Class names corrected, references updated, and a link updated by _Martin P Kidd_, Aug 14 2010