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    Combinatorics of unique maximal factorization families (UMFFs)

    135353_19064_PUB-CBS-EEB-JS-55589.pdf (215.1Kb)
    Access Status
    Open access
    Authors
    Daykin, D.
    Daykin, J.
    Smyth, Bill
    Date
    2009
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Daykin, David and Daykin, Jacqueline and Smyth, W. F. 2009. Combinatorics of Unique Maximal Factorization Families (UMFFs). Fundamenta Informaticae. 97 (3): pp. 295-309.
    Source Title
    Fundamenta Informaticae
    ISSN
    01692968
    Faculty
    Curtin Business School
    The Digital Ecosystems and Business Intelligence Institute (DEBII)
    School
    Digital Ecosystems and Business Intelligence Institute (DEBII)
    URI
    http://hdl.handle.net/20.500.11937/19951
    Collection
    • Curtin Research Publications
    Abstract

    Suppose a set W of strings contains exactly one rotation (cyclic shift) of every primitive string on some alphabet Σ. Then W is a circ-UMFF if and only if every word in Σ+ has a unique maximal factorization over W. The classic circ-UMFF is the set of Lyndon words based on lexicographic ordering (1958). Duval (1983) designed a linear sequential Lyndon factorization algorithm; a corresponding PRAM parallel algorithm was described by J. Daykin, Iliopoulos and Smyth (1994). Daykin and Daykin defined new circ-UMFFs based on various methods for totally ordering sets of strings (2003), and further described the structure of all circ-UMFFs (2008). Here we prove new combinatorial results for circ-UMFFs, and in particular for the case of Lyndon words. We introduce Acrobat and Flight Deck circ-UMFFs, and describe some of our results in terms of dictionaries. Applications of circ-UMFFs pertain to structured methods for concatenating and factoring strings over ordered alphabets, and those of Lyndon words are wide ranging and multidisciplinary.

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