Complete returns

The Sequence of Open and Closed Prefixes of a Sturmian Word

A finite word is closed if it contains a factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We are interested in the oc-sequence of a word, which is the binary sequence whose *n*-th …

The sequence of open and closed prefixes of a Sturmian word

A finite word is closed if it contains a factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We are interested in the oc-sequence of a word, which is the binary sequence whose *n*-th …

Open and Closed Prefixes of Sturmian Words

A word is closed if it contains a proper factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We deal with the sequence of open and closed prefixes of Sturmian words and prove that …

Enumeration and structure of trapezoidal words

Trapezoidal words are words having at most $n+1$ distinct factors of length $n$ for every $n\ge 0$. They therefore encompass finite Sturmian words. We give combinatorial characterizations of trapezoidal words and exhibit a formula for their …

A new characteristic property of rich words

Originally introduced and studied by the third and fourth authors together with J. Justin and S. Widmer (2008), rich words constitute a new class of finite and infinite words characterized by containing the maximal number of distinct …

Rich and Periodic-Like Words

In this paper we investigate the periodic structure of rich words (i.e., words having the highest possible number of palindromic factors), giving new results relating them with periodic-like words. In particular, some new characterizations of …