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On the distribution of characteristic parameters of words II

Published online by Cambridge University Press:  15 December 2002

Arturo Carpi  and
Aldo de Luca
Arturo Carpi
Affiliation:
Dipartimento di Matematica e Informatica, Università di Perugia, via Vanvitelli 1, 06123 Perugia, Italy; carpi@dipmat.unipg.it.
Aldo de Luca
Affiliation:
Dipartimento di Matematica dell'Università di Roma “La Sapienza”, piazzale Aldo Moro 2, 00185 Roma, Italy and Centro Interdisciplinare “B. Segre”, Accademia dei Lincei, via della Lungara 10, 00100 Roma, Italy; deluca@mat.uniroma1.it.
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Abstract

The characteristic parameters K w and R w of a word w over a finite alphabet are defined as follows: K w is the minimal natural number such that w has no repeated suffix of length K w and R w is the minimal natural number such that w has no right special factor of length R w . In a previous paper, published on this journal, we have studied the distributions of these parameters, as well as the distribution of the maximal length of a repetition, among the words of each length on a given alphabet. In this paper we give the exact values of these distributions in a special case. However, these values give upper bounds to the distributions in the general case. Moreover, we study the most frequent and the average values of the characteristic parameters and of the maximal length of a repetition over the set of all words of length n.

Keywords

Special factorcharacteristic parameterrepeated factor.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 1 , January 2002 , pp. 97 - 127
Copyright
© EDP Sciences, 2002

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References

Carpi, A. and de Luca, A., Words and special factors. Theoret. Comput. Sci. 259 (2001) 145-182. CrossRef
A. Carpi and A. de Luca, Semiperiodic words and root-conjugacy. Theoret. Comput. Sci. (to appear).
Carpi, A. and de Luca, A., Periodic-like words, periodicity, and boxes. Acta Informatica 37 (2001) 597-618. CrossRef
Carpi, A. and de Luca, A., On the distribution of characteristic parameters of words. RAIRO: Theoret. Informatics Appl. 36 (2002) 99-128.
Carpi, A., de Luca, A. and Varricchio, S., Words, univalent factors, and boxes. Acta Informatica 38 (2002) 409-436. CrossRef
Fine, N.J. and Wilf, H.S., Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109-114. CrossRef
G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers. Oxford University Press, Oxford, UK (1979).
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M. Lothaire, Combinatorics on Words, 2nd Edition. Cambridge Mathematical Library, Cambridge University Press, Cambridge, UK (1997).
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