1. Fine and Wilf words for any periods.
- Author
-
Tijdeman, R. and Zamboni, L.
- Subjects
ALGORITHMS ,ISOMORPHISM (Mathematics) ,CATEGORIES (Mathematics) ,GROUP theory - Abstract
Let
w = w be a word of maximal length1 … wn n , and with a maximal number of distinct letters for this length, such thatw has periodsp but not period gcd(1 , …, pn p ). We provide a fast algorithm to compute n and w. We show that w is uniquely determined apart from isomorphism and that it is a palindrome. Furthermore we give lower and upper bounds for n as explicit functions of1 ,…,pr p . For1 , …pr r = 2 the exact value of n is due to Fine and Wilf. In case the number of distinct letters in the extremal word equals r a formula for n had been given by Castelli, Mignosi and Restivo in caser = 3 and by Justin ifr > 3 . [Copyright &y& Elsevier]- Published
- 2003
- Full Text
- View/download PDF