On graphs of central episturmian words

AbstractEpisturmian sequences are a natural extension of Sturmian sequences to the case of finite alphabets of arbitrary cardinality. In this paper, we are interested in central episturmian words, or simply, epicentral words, i.e., the palindromic prefixes of standard episturmian sequences. An epicentral word admits a variety of faithful representations including as a directive word, as a certain type of period vector, as a Parikh vector, as a certain type of Fine and Wilf extremal word, as a suitable modular matrix, and as a labeled graph. Various interconnections between the different representations of an epicentral word are analyzed. In particular, we investigate the structure of the graphs of epicentral words proving some curious and surprising properties