Fully bordered words (Q2358697)

The characterization of binary words that have exactly two unbordered conjugates in order to show that they can be expressed as a product of two palindromes, is very well treated in this paper. The introduction section is well presented and the paper is overall easy to understand. The background theory is fully connected to the given data and the method analysis. The structure of words that do not have any other unbordered conjugate apart from the two obligatory is examined, giving an inductive characterization of fully bordered words, which shows that they have some kind of fractal structure. So, every fully bordered word is a product of two palindromes. This result can also be interpreted in terms of saying that fully bordered words have palindromic length two. An extension of the above results is directly connected to the research on critical points of a word, which is a stronger concept than unbordered conjugate: the conjugate in the critical point is always unbordered, but not vice versa.