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A000528
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Number of types of Latin squares of order n. Equivalently, number of nonisomorphic 1-factorizations of K_{n,n}.
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2
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1, 1, 1, 2, 2, 17, 324, 842227, 57810418543, 104452188344901572, 6108088657705958932053657
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| 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]
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REFERENCES
| CRC Handbook of Combinatorial Designs, 1996, p. 660.
Denes and Keedwell, Latin Squares and Applications, Academic Press 1974.
A. Hulpke, P. Kaski and P. R. J. Ostergard, The number of Latin squares of order 11, Preprint, 2009.
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LINKS
| Index entries for sequences related to Latin squares and rectangles
B. D. McKay, A. Meynert and W. Myrvold, Small Latin Squares, Quasigroups and Loops, J. Combin. Designs, to appear (2005).
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CROSSREFS
| See A040082 for another version.
Cf. A002860, A003090, A000315, A040082, A000479.
Sequence in context: A100680 A002567 A206095 * A074970 A087338 A055735
Adjacent sequences: A000525 A000526 A000527 * A000529 A000530 A000531
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KEYWORD
| hard,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Richard Bean (rwb(AT)eskimo.com), Feb 17 2004
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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