On the distribution of characteristic parameters of words

Arturo Carpi; Aldo de Luca

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 36, Issue: 1, page 67-96
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Carpi, Arturo, and de Luca, Aldo. "On the distribution of characteristic parameters of words." RAIRO - Theoretical Informatics and Applications 36.1 (2010): 67-96. <http://eudml.org/doc/92692>.

@article{Carpi2010,
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. },
author = {Carpi, Arturo, de Luca, Aldo},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Special factor; characteristic parameter; repeated factor.; finite word; finite alphabet},
language = {eng},
month = {3},
number = {1},
pages = {67-96},
publisher = {EDP Sciences},
title = {On the distribution of characteristic parameters of words},
url = {http://eudml.org/doc/92692},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Carpi, Arturo
AU - de Luca, Aldo
TI - On the distribution of characteristic parameters of words
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 1
SP - 67
EP - 96
AB - 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.
LA - eng
KW - Special factor; characteristic parameter; repeated factor.; finite word; finite alphabet
UR - http://eudml.org/doc/92692
ER -

References

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  1. A. Carpi and A. de Luca, Words and special factors. Theoret. Comput. Sci.259 (2001) 145-182.  Zbl0973.68191
  2. A. Carpi and A. de Luca, Semiperiodic words and root-conjugacy. Theoret. Comput. Sci. (to appear).  Zbl1063.68081
  3. A. Carpi and A. de Luca, Periodic-like words, periodicity, and boxes. Acta Informatica37 (2001) 597-618.  Zbl0973.68192
  4. A. Carpi and A. de Luca, On the distribution of characteristic parameters of words II. RAIRO: Theoret. Informatics Appl.36 (2002) 97-127.  Zbl1052.68106
  5. A. Carpi, A. de Luca and S. Varricchio, Words, univalent factors, and boxes. Acta Informatica38 (2002) 409-436.  Zbl1025.68052
  6. J. Cassaigne, Complexité et facteurs spéciaux. Bull. Belg. Math. Soc.4 (1997) 67-88.  
  7. A. Colosimo and A. de Luca, Special factors in biological strings. J. Theor. Biol.204 (2000) 29-46.  
  8. A. de Luca, On the combinatorics of finite words. Theoret. Comput. Sci.218 (1999) 13-39.  Zbl0916.68119
  9. H. Fredricksen, A survey of full length nonlinear shift register cycle algorithms. SIAM Rev.24 (1982) 195-221.  Zbl0482.68033
  10. L.J. Guibas and A. M. Odlyzko, Periods in strings. J. Comb. Theory (A)30 (1981) 19-42.  Zbl0464.68070
  11. M. Lothaire, Combinatorics on Words, 2nd Edition. Cambridge Mathematical Library, Cambridge University Press, Cambridge, UK (1997).  Zbl0874.20040
  12. M. Lothaire, Algebraic Combinatorics on Words. Cambridge University Press, Cambridge, UK (2002).  Zbl1001.68093
  13. R.C. Lyndon and M.P. Schützenberger, The equation aM=bNcP in a free group. Mich. Math. J.9 (1962) 289-298.  Zbl0106.02204
  14. E. Rivals and S. Rahmann, Combinatorics of periods in strings. Springer, Berlin, Lecture Notes in Comput. Sci. 2076 (2001) 615-626.  Zbl0986.68101

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