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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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On semiregular permutations of a finite set
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by Alice C. Niemeyer, Tomasz Popiel, Cheryl E. Praeger and Şükrü Yalçınkaya PDF
Math. Comp. 81 (2012), 605-622 Request permission

Abstract:

In this paper we establish upper and lower bounds for the proportion of permutations in symmetric groups which power up to semiregular permutations (permutations all of whose cycles have the same length). Provided that an integer $n$ has a divisor at most $d$, we show that the proportion of such elements in $S_n$ is at least $cn^{-1+1/2d}$ for some constant $c$ depending only on $d$ whereas the proportion of semiregular elements in $S_n$ is less than $2n^{-1}$.
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Additional Information
  • Alice C. Niemeyer
  • Affiliation: School of Mathematics and Statistics, The University of Western Australia, Perth, WA, 6009, Australia
  • Email: Alice.Niemeyer@uwa.edu.au
  • Tomasz Popiel
  • Affiliation: School of Mathematics and Statistics, The University of Western Australia, Perth, WA, 6009, Australia
  • Email: Tomasz.Popiel@uwa.edu.au
  • Cheryl E. Praeger
  • Affiliation: School of Mathematics and Statistics, The University of Western Australia, Perth, WA, 6009, Australia
  • MR Author ID: 141715
  • ORCID: 0000-0002-0881-7336
  • Email: Cheryl.Praeger@uwa.edu.au
  • Şükrü Yalçınkaya
  • Affiliation: School of Mathematics and Statistics, The University of Western Australia, Perth, WA, 6009, Australia
  • Email: sukru@maths.uwa.edu.au
  • Received by editor(s): December 10, 2009
  • Received by editor(s) in revised form: November 16, 2010
  • Published electronically: August 25, 2011
  • © Copyright 2011 American Mathematical Society
  • Journal: Math. Comp. 81 (2012), 605-622
  • MSC (2010): Primary 20B05, 20B25
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02506-8
  • MathSciNet review: 2833511