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

1, 1, 1, 2, 2, 17, 324, 842227, 57810418543, 104452188344901572, 6108088657705958932053657

Offset: 1

Author

N. J. A. Sloane

Keywords

• hard
• nonn
• nice
• more

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

There are 6108088657705958932053657 isomorphism classes of one-factorizations of K_{11,11}. - Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009

References

• CRC Handbook of Combinatorial Designs, 1996, p. 660.
• Denes and Keedwell, Latin Squares and Applications, Academic Press 1974.

Links

• A. Hulpke, Petteri Kaski and Patric R. J. Östergård, The number of Latin squares of order 11, Math. Comp. 80 (2011) 1197-1219
• B. D. McKay, A. Meynert and W. Myrvold, Small Latin Squares, Quasigroups and Loops, J. Combin. Designs, to appear (2005).
• Index entries for sequences related to Latin squares and rectangles

Crossrefs

See A040082 for another version.

Cf. A002860, A003090, A000315, A040082, A000479.

Extensions

More terms from Richard Bean, Feb 17 2004

a(11) from Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009