Search: id:A000528
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%I A000528
%S A000528 1,1,1,2,2,17,324,842227,57810418543,104452188344901572,6108088657705958932053657
%N A000528 Number of types of Latin squares of order n. Equivalently, number of 
               nonisomorphic 1-factorizations of K_{n,n}.
%C A000528 Here "type" means an equivalence class of Latin squares under the operations 
               of row permutation, column permutation, symbol permutation and transpose. 
               In the 1-factorizations formulation, these operations are labeling 
               of left side, labeling of right side, permuting the order in which 
               the factors are listed and swapping the left and right sides, respectively. 
               [Brendan McKay]
%D A000528 CRC Handbook of Combinatorial Designs, 1996, p. 660.
%D A000528 Denes and Keedwell, Latin Squares and Applications, Academic Press 1974.
%D A000528 A. Hulpke, P. Kaski and P. R. J. Ostergard, The number of Latin squares 
               of order 11, Preprint, 2009.
%H A000528 <a href="Sindx_La.html#Latin">Index entries for sequences related to 
               Latin squares and rectangles</a>
%H A000528 B. D. McKay, A. Meynert and W. Myrvold, <a href="http://cs.anu.edu.au/
               ~bdm/papers/ls_final.pdf">Small Latin Squares, Quasigroups and Loops</
               a>, J. Combin. Designs, to appear (2005).
%Y A000528 See A040082 for another version.
%Y A000528 Cf. A002860, A003090, A000315, A040082, A000479.
%Y A000528 Sequence in context: A027607 A100680 A002567 this_sequence A074970 A087338 
               A055735
%Y A000528 Adjacent sequences: A000525 A000526 A000527 this_sequence A000529 A000530 
               A000531
%K A000528 hard,nonn,nice
%O A000528 1,4
%A A000528 N. J. A. Sloane (njas(AT)research.att.com).
%E A000528 More terms from Richard Bean (rwb(AT)eskimo.com), Feb 17 2004
%E A000528 There are 6108088657705958932053657 isomorphism classes of one-factorizations 
               of $K_{11,11}$. - Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), 
               Sep 18 2009

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