On multiperiodic words

Štěpán Holub

RAIRO - Theoretical Informatics and Applications (2006)

  • Volume: 40, Issue: 4, page 583-591
  • ISSN: 0988-3754

Abstract

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In this note we consider the longest word, which has periods p1,...,pn, and does not have the period gcd(p1,...,pn). The length of such a word can be established by a simple algorithm. We give a short and natural way to prove that the algorithm is correct. We also give a new proof that the maximal word is a palindrome.

How to cite

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Holub, Štěpán. "On multiperiodic words." RAIRO - Theoretical Informatics and Applications 40.4 (2006): 583-591. <http://eudml.org/doc/249705>.

@article{Holub2006,
abstract = { In this note we consider the longest word, which has periods p1,...,pn, and does not have the period gcd(p1,...,pn). The length of such a word can be established by a simple algorithm. We give a short and natural way to prove that the algorithm is correct. We also give a new proof that the maximal word is a palindrome. },
author = {Holub, Štěpán},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Periodicity; combinatorics on words.; periodicity; combinatorics on words},
language = {eng},
month = {11},
number = {4},
pages = {583-591},
publisher = {EDP Sciences},
title = {On multiperiodic words},
url = {http://eudml.org/doc/249705},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Holub, Štěpán
TI - On multiperiodic words
JO - RAIRO - Theoretical Informatics and Applications
DA - 2006/11//
PB - EDP Sciences
VL - 40
IS - 4
SP - 583
EP - 591
AB - In this note we consider the longest word, which has periods p1,...,pn, and does not have the period gcd(p1,...,pn). The length of such a word can be established by a simple algorithm. We give a short and natural way to prove that the algorithm is correct. We also give a new proof that the maximal word is a palindrome.
LA - eng
KW - Periodicity; combinatorics on words.; periodicity; combinatorics on words
UR - http://eudml.org/doc/249705
ER -

References

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  1. M.G. Castelli, F. Mignosi and A. Restivo, Fine and Wilf's theorem for three periods and a generalization of sturmian words. Theoret. Comput. Sci.218 (1999) 83–94.  
  2. S. Constantinescu and L. Ilie, Generalised Fine and Wilf's theorem for arbitrary number of periods. Theoret. Comput. Sci.339 (2005) 49–60.  
  3. N.J. Fine and H.S. Wilf, Uniqueness theorems for periodic functions. Proc. Amer. Math. Soc.16 (1965) 109–114.  
  4. Š. Holub, A solution of the equation ( x 1 2 ⋯ x n 2 ) 3 = ( x 1 3 ⋯ x n 3 ) 2 , in Contributions to general algebra, 11 (Olomouc/Velké Karlovice, 1998), Heyn, Klagenfurt (1999) 105–111.  
  5. J. Justin, On a paper by Castelli, Mignosi, Restivo. Theoret. Inform. Appl.34 (2000) 373–377.  
  6. A. Lentin, Équations dans les monoïdes libres. Mathématiques et Sciences de l'Homme, No. 16, Mouton, (1972).  
  7. R. Tijdeman and L. Zamboni, Fine and Wilf words for any periods. Indag. Math. (N.S.)14 (2003) 135–147.  

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