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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
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OFFSET
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1,4
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COMMENTS
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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
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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REFERENCES
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CRC Handbook of Combinatorial Designs, 1996, p. 660.
Denes and Keedwell, Latin Squares and Applications, Academic Press 1974.
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LINKS
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CROSSREFS
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KEYWORD
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hard,nonn,nice,more
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AUTHOR
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EXTENSIONS
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a(11) from Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009
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STATUS
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approved
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