Recursively renewable words and coding of irrational rotations. (English) Zbl 1132.37008

Akiyama, Shigeki; Shirasaka, Masayuki

J. Math. Soc. Japan 59, No. 4, 1199-1234 (2007).

A one-sided infinite sequence over a finite alphabet is called \(k\)-renewable if there is a set of no more than \(k\) words, not all of them symbols, with the property that \(z\) is an infinite word over that set. A sequence which non-trivially permits such a decomposition infinitely often is called recursively \(k\)-renewable. Thus, for example, a Sturmian word is recursively \(2\)-renewable. Here this notion is related to sequences generated by coding irrational rotations, generalizing the combinatorial properties of Sturmian sequences. The special combinatorial properties of sequences associated to rotations with quadratic parameters are studied.

Reviewer: Thomas Ward (Norwich)

MSC:

37B10	Symbolic dynamics
68R15	Combinatorics on words
11J70	Continued fractions and generalizations
11A63	Radix representation; digital problems

Keywords:

Sturmian sequence; renewable sequence; irrational rotations