Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-27T02:51:08.731Z Has data issue: false hasContentIssue false
  • English
  • Français

On the distribution of characteristic parameters of words

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; [email protected].
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; [email protected].
Get access

Abstract

For any finite word w on a finite alphabet, we consider the basic parameters Rw and Kw of w defined as follows: Rw is the minimal natural number for which w has no right special factor of length Rw and Kw is the minimal natural number for which w has no repeated suffix of length Kw. In this paper we study the distributions of these parameters, here called characteristic parameters, among the words of each length on a fixed alphabet.

Keywords

Special factorcharacteristic parameterrepeated factor.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 1 , January 2002 , pp. 67 - 96
Copyright
© EDP Sciences, 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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 II. RAIRO: Theoret. Informatics Appl. 36 (2002) 97-127.
Carpi, A., de Luca, A. and Varricchio, S., Words, univalent factors, and boxes. Acta Informatica 38 (2002) 409-436. CrossRef
Cassaigne, J., Complexité et facteurs spéciaux. Bull. Belg. Math. Soc. 4 (1997) 67-88.
Colosimo, A. and de Luca, A., Special factors in biological strings. J. Theor. Biol. 204 (2000) 29-46. CrossRef
de Luca, A., On the combinatorics of finite words. Theoret. Comput. Sci. 218 (1999) 13-39. CrossRef
Fredricksen, H., A survey of full length nonlinear shift register cycle algorithms. SIAM Rev. 24 (1982) 195-221. CrossRef
Guibas, L.J. and Odlyzko, A. M., Periods in strings. J. Comb. Theory (A) 30 (1981) 19-42. CrossRef
M. Lothaire, Combinatorics on Words, 2nd Edition. Cambridge Mathematical Library, Cambridge University Press, Cambridge, UK (1997).
M. Lothaire, Algebraic Combinatorics on Words. Cambridge University Press, Cambridge, UK (2002).
Lyndon, R.C. and Schützenberger, M.P., The equation a M =b N c P in a free group. Mich. Math. J. 9 (1962) 289-298.
E. Rivals and S. Rahmann, Combinatorics of periods in strings. Springer, Berlin, Lecture Notes in Comput. Sci. 2076 (2001) 615-626. CrossRef