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Long cycles in abc-permutations

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Functional Analysis and Other Mathematics

Abstract

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).

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Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Igor Pak & Amanda Redlich

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  1. Igor Pak
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  2. Amanda Redlich
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Correspondence to Igor Pak.

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Pak, I., Redlich, A. Long cycles in abc-permutations. Funct. Anal. Other Math. 2, 87–92 (2008). https://doi.org/10.1007/s11853-008-0017-0

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  • DOI: https://doi.org/10.1007/s11853-008-0017-0

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