The number of Latin squares of order 11

• DOI: 10.1090/s0025-5718-2010-02420-2
• Publication Date: 2010-12-29T14:39:37Z
• Authors: Alexander Hulpke; Petteri Kaski; Patric R. J. Öste...
• Keywords: 05B15; 05C70; FOS: Mathematics; Mathematics - Combinatorics; 05C30; Combinatorics (math.CO); 05B15; 05A15; 05C30; 05C70; 0101 mathematics; 05A15; 01 natural sciences

Minor revision; to appear in Mathematics of Computation<br/>Constructive and nonconstructive techniques are employed to enumerate Latin squares and related objects. It is established that there are (i) 2036029552582883134196099 main classes of Latin squares of order 11; (ii) 6108088657705958932053657 isomorphism classes of one-factorizations of $K_{11,11}$; (iii) 12216177315369229261482540 isotopy classes of Latin squares of order 11; (iv) 1478157455158044452849321016 isomorphism classes of loops of order 11; and (v) 19464657391668924966791023043937578299025 isomorphism classes of quasigroups of order 11. The enumeration is constructive for the 1151666641 main classes with an autoparatopy group of order at least 3.<br/>