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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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

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 $3$.
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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