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.

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 $n$.

DOI : https://doi.org/10.1051/ita:2002005
Classification : 68R15,  68R05
Mots clés : special factor, characteristic parameter, repeated factor
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title = {On the distribution of characteristic parameters of words {II}},
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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/

[1] A. Carpi and A. De Luca, Words and special factors. Theoret. Comput. Sci. 259 (2001) 145-182. | MR 1832789 | Zbl 0973.68191

[2] A. Carpi and A. De Luca, Semiperiodic words and root-conjugacy. Theoret. Comput. Sci. (to appear). | MR 1964629 | Zbl 1063.68081

[3] A. Carpi and A. De Luca, Periodic-like words, periodicity, and boxes. Acta Informatica 37 (2001) 597-618. | MR 1830469 | Zbl 0973.68192

[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 1928159 | Zbl 1052.68106

[5] A. Carpi, A. De Luca and S. Varricchio, Words, univalent factors, and boxes. Acta Informatica 38 (2002) 409-436. | MR 1897479 | Zbl 1025.68052

[6] N.J. Fine and H.S. Wilf, Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109-114. | MR 174934 | Zbl 0131.30203

[7] G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers. Oxford University Press, Oxford, UK (1979). | MR 568909 | Zbl 0423.10001

[8] J.D. Kececioglu and E.W. Myers, Combinatorial algorithms for DNA sequence assembly. Algorithmica 13 (1995) 7-51. | MR 1304308 | Zbl 0831.92013

[9] M. Lothaire, Combinatorics on Words, 2nd Edition. Cambridge Mathematical Library, Cambridge University Press, Cambridge, UK (1997). | MR 1475463 | Zbl 0874.20040

[10] F. Mignosi, A. Restivo and M. Sciortino, Forbidden factors and fragment assembly. RAIRO: Theoret. Informatics Appl. (to appear). | Numdam | MR 1922296 | Zbl 1005.68122

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