Introducing privileged words – privileged complexity of Sturmian words

: privileged complexity of Sturmian words

: Jarkko Peltomäki

Publisher: Elsevier B.V.

: 2013

: Theoretical Computer Science

: TCS

: 500

: 57

: 67

: 11

: 0304-3975

DOI: https://doi.org/10.1016/j.tcs.2013.05.028

: http://www.sciencedirect.com/science/article/pii/S0304397513004027

In this paper we introduce a new class of so-called privileged words which have been previously considered only a little. We develop the basic properties of privileged words, which turn out to share similar properties with palindromes. Privileged words are studied in relation to previously studied classes of words, rich words, Sturmian words and episturmian words. A new characterization of Sturmian words is given in terms of privileged complexity. The privileged complexity of the Thue-Morse word is also briefly studied.