dc.contributor.author Daykin, D. dc.contributor.author Daykin, J. dc.contributor.author Smyth, Bill dc.date.accessioned 2017-01-30T12:16:40Z dc.date.available 2017-01-30T12:16:40Z dc.date.created 2010-03-31T20:02:38Z dc.date.issued 2009 dc.identifier.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. dc.identifier.uri http://hdl.handle.net/20.500.11937/19951 dc.description.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. dc.publisher IOS Press dc.subject UMFF dc.subject dictionary dc.subject factor dc.subject concatenate dc.subject total order dc.subject circ-UMFF dc.subject Lyndon dc.subject maximal dc.subject string dc.subject word dc.subject alphabet dc.subject lexicographic order dc.title Combinatorics of unique maximal factorization families (UMFFs) dc.type Journal Article dcterms.source.volume 97 dcterms.source.number 3 dcterms.source.startPage 295 dcterms.source.endPage 309 dcterms.source.issn 01692968 dcterms.source.title Fundamenta Informaticae curtin.department Digital Ecosystems and Business Intelligence Institute (DEBII) curtin.accessStatus Open access curtin.faculty Curtin Business School curtin.faculty The Digital Ecosystems and Business Intelligence Institute (DEBII)
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