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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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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


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 $3$.
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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:
  • 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:
  • Patric R. J. Östergård
  • Affiliation: Department of Communications and Networking, Aalto University, P.O. Box 13000, 00076 Aalto, Finland
  • Email:
  • 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:
  • MathSciNet review: 2772119