# On multiperiodic words

RAIRO - Theoretical Informatics and Applications (2006)

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

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

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