A003090 Number of species (or "main classes" or "paratopy classes") of Latin squares of order n.
1, 1, 1, 2, 2, 12, 147, 283657, 19270853541, 34817397894749939, 2036029552582883134196099
Offset: 1
References
- F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 231.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Yue Guan, Minjia Shi, Denis S. Krotov, The Steiner triple systems of order 21 with a transversal subdesign TD(3,6), arXiv:1905.09081 [math.CO], 2019.
- A. Hulpke, P. Kaski and Patric R. J. Östergård, The number of Latin squares of order 11, Math. Comp. 80 (2011) 1197-1219
- Brendan D. McKay, Latin Squares (has list of all such squares)
- Brendan D. McKay, A. Meynert and W. Myrvold, Small Latin Squares, Quasigroups and Loops, J. Combin. Designs, 15 (2007), no. 2, 98-119.
- Brendan D. McKay and E. Rogoyski, Latin squares of order ten, Electron. J. Combinatorics, 2 (1995) #N3.
- M. G. Palomo, Latin polytopes, arXiv preprint arXiv:1402.0772 [math.CO], 2014-2016.
- Giancarlo Urzua, On line arrangements with applications to 3-nets, arXiv:0704.0469 [math.AG], 2007-2009 (see page 9).
- Ian M. Wanless, A Generalization of Transversals for Latin Squares, Electronic Journal of Combinatorics, volume 9, number 1 (2002), R12.
- M. B. Wells, Elements of Combinatorial Computing, Pergamon, Oxford, 1971. [Annotated scanned copy of pages 237-240]
- Index entries for sequences related to Latin squares and rectangles
Extensions
a(9)-a(10) (from the McKay-Meynert-Myrvold article) from Richard Bean, Feb 17 2004
a(11) from Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009