Closed Ziv-Lempel factorization of the $m$-bonacci words

Abstract

A word w is said to be closed if it has a proper factor x which occurs exactly twice in w, as a prefix and as a suffix of w. Based on the concept of Ziv-Lempel factorization, we define the closed z-factorization of finite and infinite words. Then we find the closed z-factorization of the infinite m-bonacci words for all m ≥ 2. We also classify closed prefixes of the infinite m-bonacci words.