On the distribution of characteristic parameters of words II

Arturo Carpi; Aldo de Luca

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2002)

  • Volume: 36, Issue: 1, page 97-127
  • ISSN: 0988-3754

Abstract

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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 .

How to cite

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Carpi, Arturo, and Luca, Aldo de. "On the distribution of characteristic parameters of words II." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 36.1 (2002): 97-127. <http://eudml.org/doc/244751>.

@article{Carpi2002,
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 $n$.},
author = {Carpi, Arturo, Luca, Aldo de},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {special factor; characteristic parameter; repeated factor; characteristic parameters },
language = {eng},
number = {1},
pages = {97-127},
publisher = {EDP-Sciences},
title = {On the distribution of characteristic parameters of words II},
url = {http://eudml.org/doc/244751},
volume = {36},
year = {2002},
}

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
PB - EDP-Sciences
VL - 36
IS - 1
SP - 97
EP - 127
AB - 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 $n$.
LA - eng
KW - special factor; characteristic parameter; repeated factor; characteristic parameters
UR - http://eudml.org/doc/244751
ER -

References

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  1. [1] A. Carpi and A. de Luca, Words and special factors. Theoret. Comput. Sci. 259 (2001) 145-182. Zbl0973.68191MR1832789
  2. [2] A. Carpi and A. de Luca, Semiperiodic words and root-conjugacy. Theoret. Comput. Sci. (to appear). Zbl1063.68081MR1964629
  3. [3] A. Carpi and A. de Luca, Periodic-like words, periodicity, and boxes. Acta Informatica 37 (2001) 597-618. Zbl0973.68192MR1830469
  4. [4] A. Carpi and A. de Luca, On the distribution of characteristic parameters of words. RAIRO: Theoret. Informatics Appl. 36 (2002) 99-128. Zbl1052.68106MR1928159
  5. [5] A. Carpi, A. de Luca and S. Varricchio, Words, univalent factors, and boxes. Acta Informatica 38 (2002) 409-436. Zbl1025.68052MR1897479
  6. [6] N.J. Fine and H.S. Wilf, Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109-114. Zbl0131.30203MR174934
  7. [7] G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers. Oxford University Press, Oxford, UK (1979). Zbl0423.10001MR568909
  8. [8] J.D. Kececioglu and E.W. Myers, Combinatorial algorithms for DNA sequence assembly. Algorithmica 13 (1995) 7-51. Zbl0831.92013MR1304308
  9. [9] M. Lothaire, Combinatorics on Words, 2nd Edition. Cambridge Mathematical Library, Cambridge University Press, Cambridge, UK (1997). Zbl0874.20040MR1475463
  10. [10] F. Mignosi, A. Restivo and M. Sciortino, Forbidden factors and fragment assembly. RAIRO: Theoret. Informatics Appl. (to appear). Zbl1005.68122MR1922296

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