Lyndon-like and V-order factorizations of strings

Abstract

We say a family W of strings is an UMFF if every string has a unique maximal factorization over W . Then W is an UMFF iff xy , yz ∈ W and y non-empty imply xyz ∈ W . Let L-order denote lexicographic order. Danh and Daykin discovered V-order, B-order and T-order . Let R be L, V, B or T. Then we call r an R-word if it is strictly first in R-order among the cyclic permutations of r . The set of R-words form an UMFF. We show a large class of B-like UMFF. The well-known Lyndon factorization of Chen, Fox and Lyndon is the L case, and it motivated our work.