# On the distribution of characteristic parameters of words II

RAIRO - Theoretical Informatics and Applications (2010)

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

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topCarpi, Arturo, and de Luca, Aldo. "On the distribution of characteristic parameters of words II." RAIRO - Theoretical Informatics and Applications 36.1 (2010): 97-127. <http://eudml.org/doc/92693>.

@article{Carpi2010,

abstract = {
The characteristic parameters Kw and Rw of a word w
over a finite alphabet are defined as follows: Kw is the
minimal natural number such that w has no repeated suffix of
length Kw and Rw is the minimal natural number such that
w has no right special factor of length Rw. 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, de Luca, Aldo},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Special factor; characteristic parameter; repeated factor.; repeated factor; characteristic parameters },

language = {eng},

month = {3},

number = {1},

pages = {97-127},

publisher = {EDP Sciences},

title = {On the distribution of characteristic parameters of words II},

url = {http://eudml.org/doc/92693},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Carpi, Arturo

AU - de Luca, Aldo

TI - On the distribution of characteristic parameters of words II

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 36

IS - 1

SP - 97

EP - 127

AB -
The characteristic parameters Kw and Rw of a word w
over a finite alphabet are defined as follows: Kw is the
minimal natural number such that w has no repeated suffix of
length Kw and Rw is the minimal natural number such that
w has no right special factor of length Rw. 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.; repeated factor; characteristic parameters

UR - http://eudml.org/doc/92693

ER -

## References

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- A. Carpi and A. de Luca, Semiperiodic words and root-conjugacy. Theoret. Comput. Sci. (to appear).
- A. Carpi and A. de Luca, Periodic-like words, periodicity, and boxes. Acta Informatica37 (2001) 597-618.
- A. Carpi and A. de Luca, On the distribution of characteristic parameters of words. RAIRO: Theoret. Informatics Appl.36 (2002) 99-128.
- A. Carpi, A. de Luca and S. Varricchio, Words, univalent factors, and boxes. Acta Informatica38 (2002) 409-436.
- N.J. Fine and H.S. Wilf, Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc.16 (1965) 109-114.
- G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers. Oxford University Press, Oxford, UK (1979).
- J.D. Kececioglu and E.W. Myers, Combinatorial algorithms for DNA sequence assembly. Algorithmica13 (1995) 7-51.
- M. Lothaire, Combinatorics on Words, 2nd Edition. Cambridge Mathematical Library, Cambridge University Press, Cambridge, UK (1997).
- F. Mignosi, A. Restivo and M. Sciortino, Forbidden factors and fragment assembly. RAIRO: Theoret. Informatics Appl. (to appear).

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