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    On products of long cycles: short cycle dependence and separation probabilities

    Feray, V. and Rattan, Amarpreet (2015) On products of long cycles: short cycle dependence and separation probabilities. Journal of Algebraic Combinatorics 42 (1), pp. 183-224. ISSN 0925-9899.

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    Abstract

    We present various results on multiplying cycles in the symmetric group. One result is a generalisation of the following theorem of Boccara (1980): the number of ways of writing an odd permutation in the symmetric group on n symbols as a product of an n-cycle and an (n − 1)-cycle is independent of the permutation chosen. We give a number of different approaches of our generalisation. One partial proof uses an inductive method which we also apply to other problems. In particular, we give a formula for the distribution of the number of cycles over all products of cycles of fixed lengths. Another application is related to the recent notion of separation probabilities for permutations introduced by Bernardi, Du, Morales and Stanley (2014).

    Metadata

    Item Type: Article
    Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s10801-014-0578-6
    Keyword(s) / Subject(s): Symmetric group, Products of cycles, Separation probabilities
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Amarpreet Rattan
    Date Deposited: 23 Jun 2015 07:50
    Last Modified: 22 Aug 2016 15:17
    URI: http://eprints.bbk.ac.uk/id/eprint/12399

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