On semiregular permutations of a finite set

Alice C. Niemeyer, Tomasz Popiel, Cheryl E. Praeger, Şükr̈u Yalçinkaya

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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 c n-1+1/2d for some constant c depending only on d whereas the proportion of semiregular elements in S n is less than 2 n-1.

Original languageEnglish
Pages (from-to)605-622
Number of pages18
JournalMathematics of Computation
Volume92
Issue number341
DOIs
Publication statusPublished - 2011
Externally publishedYes

Keywords

  • Derangements
  • Generating function
  • Semiregular permutations

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