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

    Feray, V. and Rattan, Amarpreet (2014) On products of long cycles: short cycle dependence and separation probabilities. Technical Report. Birkbeck, University of London, London, UK.

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    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).


    Item Type: Monograph (Technical Report)
    Additional Information: Birkbeck Pure Mathematics Preprint Series #3
    School: Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School
    Depositing User: Administrator
    Date Deposited: 22 Mar 2019 13:18
    Last Modified: 02 Aug 2023 17:49


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