Counting occurrences for a finite set of words: an inclusion-exclusion approach - GREYC amacc Access content directly
Conference Papers Year : 2007

Counting occurrences for a finite set of words: an inclusion-exclusion approach

Abstract

In this paper, 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 give a complete proof validating the use of the inclusion-exclusion principle and compare the complexity of the method proposed here with the one using automata for solving the problem.
Fichier principal
Vignette du fichier
dmAH0103.pdf (179.92 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

hal-00452702 , version 1 (02-02-2010)
hal-00452702 , version 2 (17-08-2015)

Identifiers

Cite

Frédérique Bassino, Julien Clément, J. Fayolle, P. Nicodème. Counting occurrences for a finite set of words: an inclusion-exclusion approach. 2007 Conference on Analysis of Algorithms, AofA 07, 2007, Juan les Pins, France. pp.31-46, ⟨10.46298/dmtcs.3543⟩. ⟨hal-00452702v2⟩
1091 View
745 Download

Altmetric

Share

Gmail Facebook X LinkedIn More