Open and Closed Words

Combinatorics on words aims at finding deep connections between propertiesof sequences. The resulting theoretical findings are often used in thedesign of efficient combinatorial algorithms for string processing, but mayalso have independent interest, especially in connection with other areas ofdiscrete mathematics. The property we discuss here is, for a given finiteword, that of being closed. A finite word is called closed if it has length ≤ 1or it contains a proper factor (substring) that occurs both as a prefix and as asuffix but does not have internal occurrences. Otherwise the word is calledopen. We illustrate several aspects of open and closed words and factors,and propose some open problems.