F. Mignosi has proved that a Sturmian word has finite index if and only if the coefficients of the continued fraction development of its slope are bounded.
A Sturmian word has bounded index if and only if the continued fraction expansion of its slope has bounded partial quotients. An initial contribution to this ...
... A basic result on indexes of Sturmian word is: Proposition 5.4. (See [2] ) Every nonempty factor of a Sturmian word has a finite index. ...
A binary word ω is called Sturmian if p ( n ) = n + 1 for all n ≥ 1 . Thus among all aperiodic words, Sturmian words are those having the smallest complexity.
The Fibonacci word is an example of a Sturmian word. The start of the cutting sequence shown here illustrates the start of the word 0100101001. Contents.
Sturmian sequences are aperiodic words of minimal combinatorial complexity. These se- quences admit several equivalent definitions; for example, ...
F. Mignosi has proved that a Sturmian word has finite index if and only if the coefficients of the continued fraction development of its slope are bounded.
Jul 8, 2022 · In this note, we provide an elementary combinatorial proof of the result of Bell and Shallit and give an exact formula for the Lie complexity of ...
Aug 4, 2013 · Sturmian words are infinite words over a binary alphabet that have exactly n + 1 factors of length n for each n ≥ 0.
Combinatorics on words plays a fundamental role in various fields of mathematics, not to mention its relevance in theoretical computer science and physics.