Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On semiregular permutations of a finite set


Authors: Alice C. Niemeyer, Tomasz Popiel, Cheryl E. Praeger and Şükrü Yalçınkaya
Journal: Math. Comp. 81 (2012), 605-622
MSC (2010): Primary 20B05, 20B25
Published electronically: August 25, 2011
MathSciNet review: 2833511
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 20B05, 20B25

Retrieve articles in all journals with MSC (2010): 20B05, 20B25


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
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

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02506-8
PII: S 0025-5718(2011)02506-8
Keywords: Semiregular permutations, derangements, generating function
Received by editor(s): December 10, 2009
Received by editor(s) in revised form: November 16, 2010
Published electronically: August 25, 2011
Article copyright: © Copyright 2011 American Mathematical Society