cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A000528 Number of types of Latin squares of order n. Equivalently, number of nonisomorphic 1-factorizations of K_{n,n}.

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%I A000528 #30 Mar 12 2022 21:40:50
%S A000528 1,1,1,2,2,17,324,842227,57810418543,104452188344901572,
%T A000528 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_
%C A000528 There are 6108088657705958932053657 isomorphism classes of one-factorizations of K_{11,11}. - Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009
%D A000528 CRC Handbook of Combinatorial Designs, 1996, p. 660.
%D A000528 Denes and Keedwell, Latin Squares and Applications, Academic Press 1974.
%H A000528 A. Hulpke, Petteri Kaski and Patric R. J. Östergård, <a href="http://dx.doi.org/10.1090/S0025-5718-2010-02420-2">The number of Latin squares of order 11</a>, Math. Comp. 80 (2011) 1197-1219
%H A000528 B. D. McKay, A. Meynert and W. Myrvold, <a href="http://users.cecs.anu.edu.au/~bdm/papers/ls_final.pdf">Small Latin Squares, Quasigroups and Loops</a>, J. Combin. Designs, to appear (2005).
%H A000528 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>
%Y A000528 See A040082 for another version.
%Y A000528 Cf. A002860, A003090, A000315, A040082, A000479.
%K A000528 hard,nonn,nice,more
%O A000528 1,4
%A A000528 _N. J. A. Sloane_
%E A000528 More terms from _Richard Bean_, Feb 17 2004
%E A000528 a(11) from Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009