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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.
Cited literature [24 references]
https://hal.inria.fr/hal-00452702
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Submitted on : Monday, August 17, 2015 - 4:59:57 PM
Last modification on : Sunday, June 26, 2022 - 12:03:58 PM
Long-term archiving on: : Wednesday, November 18, 2015 - 12:17:44 PM
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Monday, August 17, 2015 - 4:59:57 PM
Last modification on : Sunday, June 26, 2022 - 12:03:58 PM
Long-term archiving on: : Wednesday, November 18, 2015 - 12:17:44 PM
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