Please use this identifier to cite or link to this item: https://doi.org/10.1080/10236190500376326
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dc.titleExtension of Goulden-Jackson cluster method on pattern occurrences in random sequences and comparison with Régnier-Szpankowski method
dc.contributor.authorKong, Y.
dc.date.accessioned2014-10-28T02:35:06Z
dc.date.available2014-10-28T02:35:06Z
dc.date.issued2005-12
dc.identifier.citationKong, Y. (2005-12). Extension of Goulden-Jackson cluster method on pattern occurrences in random sequences and comparison with Régnier-Szpankowski method. Journal of Difference Equations and Applications 11 (15) : 1265-1271. ScholarBank@NUS Repository. https://doi.org/10.1080/10236190500376326
dc.identifier.issn10236198
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/103256
dc.description.abstractThe Goulden-Jackson cluster method is a powerful method to find generating functions of pattern occurrences in random sequences [1]. The method is clearly explained, extended and implemented by Noonan and Zeilberger [2]. In this paper, we elaborate on one of the several extensions in [2], namely the extension from symmetrical Bernoulli sequences where the occurrences of each symbol have equal probability, to asymmetrical Bernoulli sequences with different probabilities of symbol generations. An explicit formula is derived for the extension, which is implicitly embedded in the treatment of [2]. The extended result is then compared with the method of Régnier-Szpankowski [3], a method which was developed independently to tackle the same problem. By manipulating some matrix inversions, we show that the Régnier-Szpankowski method can be simplified to the extended Goulden-Jackson method.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1080/10236190500376326
dc.sourceScopus
dc.subjectCorrelation polynomials
dc.subjectFrequency of pattern occurrences
dc.subjectGenerating functions
dc.subjectGoulden-Jackson cluster method
dc.subjectMatrix inversion
dc.typeArticle
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1080/10236190500376326
dc.description.sourcetitleJournal of Difference Equations and Applications
dc.description.volume11
dc.description.issue15
dc.description.page1265-1271
dc.identifier.isiut000234428200003
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