Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-05T09:48:48.743Z Has data issue: false hasContentIssue false

On multiperiodic words

Published online by Cambridge University Press:  08 November 2006

Štěpán Holub*
Affiliation:
Department of Algebra, Charles University, Sokolovská 83, 175 86 Praha, Czech Republic; [email protected]
Get access

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.

Type
Research Article
Copyright
© EDP Sciences, 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Castelli, M.G., Mignosi, F. and Restivo, A., Fine and Wilf's theorem for three periods and a generalization of sturmian words. Theoret. Comput. Sci. 218 (1999) 8394. CrossRef
Constantinescu, S. and Ilie, L., Generalised Fine and Wilf's theorem for arbitrary number of periods. Theoret. Comput. Sci. 339 (2005) 4960. CrossRef
Fine, N.J. and Wilf, H.S., Uniqueness theorems for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109114. CrossRef
Š. Holub, A solution of the equation $(x\sb 1\sp 2\cdots x\sb n\sp 2)\sp 3=(x\sb 1\sp 3\cdots x\sb n\sp 3)\sp 2$ , in Contributions to general algebra, 11 (Olomouc/Velké Karlovice, 1998), Heyn, Klagenfurt (1999) 105–111.
Justin, J., On a paper by Castelli, Mignosi, Restivo. Theoret. Inform. Appl. 34 (2000) 373377. CrossRef
A. Lentin, Équations dans les monoïdes libres. Mathématiques et Sciences de l'Homme, No. 16, Mouton, (1972).
Tijdeman, R. and Zamboni, L., Fine and Wilf words for any periods. Indag. Math. (N.S.) 14 (2003) 135147. CrossRef