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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Enumeration of racks and quandles up to isomorphism
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by Petr Vojtěchovský and Seung Yeop Yang HTML | PDF
Math. Comp. 88 (2019), 2523-2540 Request permission


Racks and quandles are prominent set-theoretical solutions of the Yang-Baxter equation. We enumerate racks and quandles of orders $n\le 13$ up to isomorphism, improving upon the previously known results for $n\le 8$ and $n\le 9$, respectively. The enumeration is based on the classification of subgroups of small symmetric groups up to conjugation, on a representation of racks and quandles in symmetric groups due to Joyce and Blackburn, and on a number of theoretical and computational observations concerning the representation. We explicitly find representatives of isomorphism types of racks of order $\le 11$ and quandles of order $\le 12$. For the remaining orders we merely count the isomorphism types, relying in part on the enumeration of $2$-reductive racks and $2$-reductive quandles due to Jedlička, Pilitowska, Stanovský, and Zamojska-Dzienio.
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Additional Information
  • Petr Vojtěchovský
  • Affiliation: Department of Mathematics, University of Denver, 2390 S York St, Denver, Colorado, 80208
  • MR Author ID: 650320
  • Email:
  • Seung Yeop Yang
  • Affiliation: Department of Mathematics, Kyungpook National University, Daegu, 41566, Republic of Korea
  • MR Author ID: 1111587
  • Email:
  • Received by editor(s): May 22, 2018
  • Received by editor(s) in revised form: September 25, 2018
  • Published electronically: January 7, 2019
  • Additional Notes: The first author was supported by a 2015 PROF grant of the University of Denver.
  • © Copyright 2019 American Mathematical Society
  • Journal: Math. Comp. 88 (2019), 2523-2540
  • MSC (2010): Primary 16T25, 20N05, 57M27
  • DOI:
  • MathSciNet review: 3957904