Long cycles in abc-permutations

  • Igor Pak
  • Amanda Redlich


An abc-permutation is a permutation σ abc S n obtained by exchanging an initial block of length a and a final block of length c of {1,…,n}, where n=a+b+c. In this note we compute the limit of the probability that a random abc-permutation is a long cycle. This resolves Arnold’s open problem (Arnold in Arnold’s problems, 2004, p. 144).


Interval exchange transformations Random permutations 

Mathematics Subject Classification (2000)

05D40 11K99 37A05 60C05 


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Copyright information

© PHASIS GmbH and Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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