On multiset of factors of a word

Given two strings, we investigate the conditions under which they have common multiset of factors of a fixed length. We show that if two strings have the same multiset of factors of length less than or equal to k then they have a common prefix and suffix of length k - 1. We also show that if two strings have the same multiset of factors of length k and k 1 then they also have the same multiset of factors of length less than k - 1. (C) 2012 Elsevier B.V. All rights reserved.