Advertisement

Number of factors in K-cycle decompositions of permutations

  • Marcel Herzog
  • K. B. Reid
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 560)

Abstract

Let π be a permutation in Sn, the symmetric group on n letters. Let k be an integer, 2 ⩽ k ⩽ n, and suppose that π can be represented as a product of k-cycles. Denote by fk(π) the minimal number of k-cycles required for such a representation. In this paper bounds for fk(π) are derived. These bounds are used to determine \(\mathop {\lim }\limits_{n \to \infty }\) for all k, where fk(n)=max{fk(π) | π ε Sn}.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    E. Bertram, Even permutations as a product of two conjugate cycles, J. Comb. Theory (A) 12 (1972), 368–380.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    J.L. Brenner, M. Randall and J. Riddell, Covering theorems for finite non-abelian simple groups, I, Colloq. Math. (Warsaw) 32 (1974), 39–48.MathSciNetMATHGoogle Scholar
  3. [3]
    M. Herzog and K.B. Reid, Representation of permutations as products of cycles of fixed length, J. Austral. Math. Soc. (to appear).Google Scholar
  4. [4]
    R. Ree, A theorem on permutations, J. Comb. Theory, 10 (1971), 174–175.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Marcel Herzog
    • 1
    • 2
    • 3
    • 4
  • K. B. Reid
    • 1
    • 2
    • 3
    • 4
  1. 1.Department of Mathematics, Institute of Advanced StudiesAustralian National UniversityCanberra
  2. 2.Department of MathematicsTel-Aviv UniversityTel AvivIsrael
  3. 3.Department of Mathematics, Institute of Advanced StudiesAustralian National UniversityCanberra
  4. 4.Departmen tof MathematicsLouisiana State UniversityBaton Rouge

Personalised recommendations