On the distribution of characteristic parameters of words II

Carpi, Arturo; Luca, Aldo de

doi:10.1051/ita:2002005

Carpi, Arturo ; Luca, Aldo de

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 1, pp. 97-127.

Résumé

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 $n$ .

MR Zbl | 2 citations dans Numdam

DOI : 10.1051/ita:2002005

Classification : 68R15, 68R05
Mots-clés : special factor, characteristic parameter, repeated factor

@article{ITA_2002__36_1_97_0,
     author = {Carpi, Arturo and Luca, Aldo de},
     title = {On the distribution of characteristic parameters of words {II}},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {97--127},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {1},
     year = {2002},
     doi = {10.1051/ita:2002005},
     mrnumber = {1928160},
     zbl = {1052.68106},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita:2002005/}
}

TY  - JOUR
AU  - Carpi, Arturo
AU  - Luca, Aldo de
TI  - On the distribution of characteristic parameters of words II
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2002
SP  - 97
EP  - 127
VL  - 36
IS  - 1
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita:2002005/
DO  - 10.1051/ita:2002005
LA  - en
ID  - ITA_2002__36_1_97_0
ER  -

%0 Journal Article
%A Carpi, Arturo
%A Luca, Aldo de
%T On the distribution of characteristic parameters of words II
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2002
%P 97-127
%V 36
%N 1
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ita:2002005/
%R 10.1051/ita:2002005
%G en
%F ITA_2002__36_1_97_0

Carpi, Arturo; Luca, Aldo de. On the distribution of characteristic parameters of words II. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 1, pp. 97-127. doi : 10.1051/ita:2002005. http://www.numdam.org/articles/10.1051/ita:2002005/

Bibliographie
Cité par

[1] A. Carpi and A. De Luca, Words and special factors. Theoret. Comput. Sci. 259 (2001) 145-182. | MR | Zbl

[2] A. Carpi and A. De Luca, Semiperiodic words and root-conjugacy. Theoret. Comput. Sci. (to appear). | MR | Zbl

[3] A. Carpi and A. De Luca, Periodic-like words, periodicity, and boxes. Acta Informatica 37 (2001) 597-618. | MR | Zbl

[4] A. Carpi and A. De Luca, On the distribution of characteristic parameters of words. RAIRO: Theoret. Informatics Appl. 36 (2002) 99-128. | Numdam | MR | Zbl

[5] A. Carpi, A. De Luca and S. Varricchio, Words, univalent factors, and boxes. Acta Informatica 38 (2002) 409-436. | MR | Zbl

[6] N.J. Fine and H.S. Wilf, Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109-114. | MR | Zbl

[7] G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers. Oxford University Press, Oxford, UK (1979). | MR | Zbl

[8] J.D. Kececioglu and E.W. Myers, Combinatorial algorithms for DNA sequence assembly. Algorithmica 13 (1995) 7-51. | MR | Zbl

[9] M. Lothaire, Combinatorics on Words, 2nd Edition. Cambridge Mathematical Library, Cambridge University Press, Cambridge, UK (1997). | MR | Zbl

[10] F. Mignosi, A. Restivo and M. Sciortino, Forbidden factors and fragment assembly. RAIRO: Theoret. Informatics Appl. (to appear). | Numdam | MR | Zbl

Cité par Sources :