## The number of Latin squares of order 11

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- by Alexander Hulpke, Petteri Kaski and Patric R. J. Östergård PDF
- Math. Comp.
**80**(2011), 1197-1219 Request permission

## 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$$;$ (ii) $6108088657705958932053657$ isomorphism classes of one-factorizations of $K_{11,11}$$;$ (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 $3$.## References

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## Additional Information

**Alexander Hulpke**- Affiliation: Department of Mathematics, Colorado State University, 1874 Campus Delivery, Fort Collins, Colorado 80523-1874
- MR Author ID: 600556
- ORCID: 0000-0002-5210-6283
- Email: hulpke@math.colostate.edu
**Petteri Kaski**- Affiliation: Helsinki Institute for Information Technology HIIT, University of Helsinki, Department of Computer Science, P.O. Box 68, 00014 University of Helsinki, Finland
- Email: petteri.kaski@cs.helsinki.fi
**Patric R. J. Östergård**- Affiliation: Department of Communications and Networking, Aalto University, P.O. Box 13000, 00076 Aalto, Finland
- Email: patric.ostergard@tkk.fi
- Received by editor(s): September 18, 2009
- Received by editor(s) in revised form: February 4, 2010
- Published electronically: September 13, 2010
- © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**80**(2011), 1197-1219 - MSC (2010): Primary 05B15, 05A15, 05C30, 05C70
- DOI: https://doi.org/10.1090/S0025-5718-2010-02420-2
- MathSciNet review: 2772119