Counting occurrences for a finite set of words: combinatorial methods - GREYC amacc Access content directly
Journal Articles ACM Transactions on Algorithms Year : 2012

Counting occurrences for a finite set of words: combinatorial methods

Abstract

In this article, we give the multivariate generating function counting texts according to their length and to the number of occurrences of words from a finite set. The application of the inclusion- exclusion principle to word counting due to Goulden and Jackson (1979, 1983) is used to derive the result. Unlike some other techniques which suppose that the set of words is reduced (i.e., where no two words are factor of one another), the finite set can be chosen arbitrarily. Noonan and Zeilberger (1999) already provided a Maple package treating the non-reduced case, without giving an expression of the generating function or a detailed proof. We provide a complete proof validating the use of the inclusion-exclusion principle. We also restate in modern terms the normal limit laws theorems of Bender and Kochman (1993), emphasising on the underlying analytic mean shifting method.
Fichier principal
Vignette du fichier
talg2010.pdf (670.47 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00452694 , version 1 (02-02-2010)
hal-00452694 , version 2 (04-02-2011)

Identifiers

Cite

Frédérique Bassino, Julien Clément, Pierre Nicodème. Counting occurrences for a finite set of words: combinatorial methods. ACM Transactions on Algorithms, 2012, 8, pp.31:1--31:28. ⟨10.1145/2229163.2229175⟩. ⟨hal-00452694v2⟩
835 View
417 Download

Altmetric

Share

Gmail Facebook X LinkedIn More