On the frequency of letters in morphic sequences. (English) Zbl 1185.68398

Saari, Kalle

Grigoriev, Dima (ed.) et al., Computer science – theory and applications. First international computer science symposium in Russia, CSR 2006, St. Petersburg, Russia, June 8–12, 2006. Proceedings. Berlin: Springer (ISBN 3-540-34166-8/pbk). Lecture Notes in Computer Science 3967, 334-345 (2006).

Summary: A necessary and sufficient criterion for the existence and value of the frequency of a letter in a morphic sequence is given. This is done using a certain incidence matrix associated with the morphic sequence. The characterization gives rise to a simple if-and-only-if condition that all letter frequencies exist.
For the entire collection see [Zbl 1102.68006].

MSC:

68Q45	Formal languages and automata
68R15	Combinatorics on words

Keywords:

morphic sequences; HD0L sequences; frequency of letters; incidence matrix; simple generator