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    Enumeration of noncrossing pairings on bit strings

    Rattan, Amarpreet and Kemp, T. and Mahlburg, K. and Smyth, C. (2011) Enumeration of noncrossing pairings on bit strings. Journal of Combinatorial Theory, Series A 118 (1), pp. 129-151. ISSN 0097-3165.

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    Abstract

    A non-crossing pairing on a bitstring matches 1s and 0s in a manner such that the pairing diagram is nonintersecting. By considering such pairings on arbitrary bitstrings we generalize classical problems from the theory of Catalan structures. In particular, it is very difficult to find useful explicit formulas for the enumeration function which counts the number of pairings as a function of the underlying bitstring. We determine explicit formulas for enumeration function for bit strings, and also prove general upper bounds in terms of Fuss-Catalan numbers by relating non-crossing pairings to other generalized Catalan structures (that are in some sense more natural). This enumeration problem arises in the theory of random matrices and free probability.

    Metadata

    Item Type: Article
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hall
    Date Deposited: 28 Apr 2014 09:46
    Last Modified: 22 Aug 2016 15:17
    URI: https://eprints.bbk.ac.uk/id/eprint/9619

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