A standard correspondence on epicentral words

• Authors: Aldo De Luca
• Venue: European Journal of Combinatorics
• Year: 2012

Central words are the palindromic prefixes of all standard Sturmian words. In 1997, the author introduced two different methods to generate central words. The first is based on the iteration of the right-palindromic closure operator and the second on the iteration of two standard morphisms, i.e., the Fibonacci morphism F and F@?E, where E is the interchange morphism. Moreover, it was proved that there exists a basic relation, called standard correspondence, between these two constructions. In this paper, we give an extension of the standard correspondence to the case of epicentral words, i.e., the palindromic prefixes of the standard episturmian words, introduced by Droubay et al. in 2001. Several interesting combinatorial properties of this correspondence and of some bijective operators associated to it are proved. Finally, some relations existing between the representations of epicentral words by Parikh vectors, period vectors, and trees are shown.