Fibonacci字与Fine-Wilf定理的推广

Fibonacci Words and a Generalization of Fine-Wilf Theorem

从任意两个Fibonacci字之间的公共前缀长度的研究出发,讨论了其与字的组合学中重要定理-Fine-W ilf定理的关系;用初等数论知识对Fine-W ilf定理进行了推广,得出:设u和v是A上的两个字,gcd(|u|,|v|)=1,若存在p、q使得up和vq有长度至少为|u|+|v|-k的公共前缀,则u和v中至多出现k个不同的字母.

The length of common prefix between two arbitrary Fibonacci words has been investigated,and the relation between such words and Fine-Wilf Theorem has been discussed.After a generalization of Fine-Wilf Theorem by using elementary number theory,it is obtained: suppose u and v are two words over A,and gcd(|u|,|v|)=1;if there exist p and q that make up and vq have a common prefix with a length of at least |u|+|v|-k,then there are at most k distinct letters that can occur in u and v.