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- [2104. 09239] Abstract
Subsequently, Berthé, Holton and Zamboni [??] established that any Sturmian word, whose slope has a bounded continued fraction expansion, has infinitely many prefixes which are (2+ {\varepsilon}) -powers of blocks, for some positive real number {\varepsilon} depending only on the word
- arXiv:2504. 13636v1 [math. CO] 18 Apr 2025
We introduce the notion of α-numbers and formal intercept of sturmian words, and derive from this study general factorisations formula for sturmian words Sturmian words are defined as infinite words with lowest unbound complexity, and are characterized by two parameters, the first one being well-known as the slope, and the second being their formal intercepts We build this formalism by a
- Sturmian words with balanced construction - DiVA
The Kolakoski word is defined as one of the two fixed points of the run-length encoding ∆; see [5, 6] These words are identical with their own run-length encoding sequences The one beginning with 2 is: K = 2211212212211211221211212211211212212211212212 · · ·
- arXiv:1411. 5474v2 [cs. DM] 26 May 2015
Introduction In 2003 Damanik and Lenz [6] completely described factors of length n of a Sturmian word which occur as pth powers for every n ≥ 0 and p 1 Damanik and Lenz prove a series of results concerning how factors of a Sturmian ≥ word align to the corresponding (finite) standard words By a careful analysis of the alignment, they obtain the complete description of powers thanks to
- Digital lines, Sturmian words, and continued fractions - DiVA
Cover image: Eight digital straight line segments illustrating the equiv-alence relation based on the run length on all digitization levels (as de-fined in Paper IV), restricted to the first four levels The eight possible forms of S with the length specification (1, 2,2,3)
- Combinatorial structure of Sturmian words and continued fraction . . .
Let be the continued fraction expansion of an irrational real number It is well-known that the characteristic Sturmian word of slope is the limit of a sequence of finite words , with of length (the denominator of the -th convergent to ) being a suitable concatenation of copies of and one copy of
- Combinatorial structure of Sturmian words and continued fraction . . .
Let θ = [0; a 1, a 2, ⋯] be the continued fraction expansion of an irrational real number θ ∈ (0, 1) It is well-known that the characteristic Sturmian word of slope θ is the limit of a sequence of finite words (M k) k ≥ 0, with M k of length q k (the denominator of the k -th convergent to θ) being a suitable concatenation of a k copies of M k - 1 and one copy of M k - 2 Our first
- Combinatorial structure of Sturmian words and continued fraction . . .
Let θ = [0; a 1 , a 2 , ] be the continued fraction expansion of an irrational real number θ ∈ (0, 1) It is well-known that the characteristic Sturmian word of slope θ is the limit of a sequence of finite words (M k) k≥0 , with M k of length q k (the denominator of the k-th convergent to θ) being a suitable concatenation of a k copies of M k−1 and one copy of M k−2 Our first
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