Name
Abstract | ||
|---|---|---|
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,K-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. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1090/S0025-5718-2010-02420-2 | MATHEMATICS OF COMPUTATION |
Keywords | Field | DocType |
Enumeration,Latin square,main class | Combinatorics,Constructive,Enumeration,Latin square,Isomorphism,Isotopy,Numerical analysis,Quasigroup,Mathematics | Journal |
Volume | Issue | ISSN |
80 | 274 | 0025-5718 |
Citations | PageRank | References |
15 | 1.09 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexander Hulpke | 1 | 64 | 9.89 |
| Petteri Kaski | 2 | 912 | 66.03 |
| Patric R. J. Östergård | 3 | 609 | 70.61 |