In mathematics, a Sturmian word (Sturmian sequence or billiard sequence), named after Jacques Charles François Sturm, is a certain kind of infinitely...
14 KB (1,939 words) - 13:42, 10 January 2025
addition. It is a paradigmatic example of a Sturmian word and specifically, a morphic word. The name "Fibonacci word" has also been used to refer to the members...
14 KB (1,938 words) - 20:16, 18 May 2025
In mathematics, a Sturmian sequence may refer to: A Sturmian word: a sequence with minimal complexity function A sequence used to determine the number...
244 bytes (66 words) - 17:57, 10 February 2011
Complexity function (redirect from Balanced word)
complexity function at most n+1. A Sturmian word over a binary alphabet is one with complexity function n + 1. A sequence is Sturmian if and only if it is balanced...
10 KB (1,313 words) - 03:08, 26 March 2025
"compact variant" It is conjectured that the Fibonacci word fractal appears for every sturmian word for which the slope, written in continued fraction expansion...
9 KB (1,116 words) - 15:37, 30 November 2024
different irrational number. Beatty sequences can also be used to generate Sturmian words. Any irrational number r {\displaystyle r} that is greater than one...
13 KB (2,174 words) - 13:07, 16 January 2025
where z is a letter not in A. Cutting sequence Lyndon word Hall word Sturmian word Lothaire (2005) p.524 Lothaire (2011) p. 10 Honkala (2010) p.505 Lothaire...
6 KB (664 words) - 15:27, 20 December 2024
another name for eigenvector of a matrix Characteristic word, a subclass of Sturmian word Euler characteristic, a topological invariant Method of characteristics...
2 KB (260 words) - 21:31, 9 May 2025
the Lyndon words. Lexicographically minimal string rotation Morphic word Sturmian word Necklace (combinatorics) Lyndon (1954). Shirshov (1953). Berstel &...
21 KB (2,749 words) - 01:18, 7 August 2024
are always at most three different intervals separating the tones. A Sturmian word is infinite sequences of two symbols (for instance, "H" and "V") describing...
25 KB (3,013 words) - 11:30, 5 January 2025
individual grid lines crossed ("cut") as a curve crosses a square grid. Sturmian words are a special case of cutting sequences where the curves are straight...
2 KB (120 words) - 07:45, 28 May 2023
periodic (meaning periodic after some nonperiodic initial segment). All Sturmian words are uniformly recurrent. Lothaire (2011) p. 30 Allouche & Shallit...
4 KB (423 words) - 05:34, 13 May 2024
number for which the digits with respect to some fixed base form a Sturmian word. The Prouhet–Thue–Morse constant and the related rabbit constant. The...
52 KB (6,816 words) - 13:34, 18 May 2025
Combinatorics on words (redirect from Word combinatorics)
equivalent definitions of Sturmian words. For example, an infinite word is Sturmian if and only if it has n + 1 {\displaystyle n+1} distinct factors of...
20 KB (2,588 words) - 12:32, 13 February 2025
resonant tunneling diode oscillators Phase-locked loop Kuramoto model Sturmian word Arnol'd, V.I. (1961). "Small denominators. I. Mapping the circle onto...
21 KB (3,182 words) - 17:11, 25 May 2025
word, a sequence such that any factor (consecutive subsequence) that appears does so infinitely often, such as the Thue–Morse sequence or a Sturmian word...
302 bytes (71 words) - 20:05, 28 October 2012
Chiara; Mignosi, Filippo; Shallit, Jeffrey; Venturini, Ilaria (2004), "Sturmian graphs and a conjecture of Moser", in Calude, Cristian S.; Calude, Elena;...
8 KB (972 words) - 06:30, 14 April 2025
finite Sturmian words, described in the previous section) Fine and Wilf's theorem can also be used to reason about the solution sets of word equations...
14 KB (2,424 words) - 20:02, 24 May 2025
of real numbers encoded by lines of tiles (the encoding is related to Sturmian sequences made as the differences of consecutive elements of Beatty sequences)...
30 KB (3,508 words) - 12:34, 5 March 2025
Mohammad-Noori, M.; Currie, James D. (2007), "Dejean's conjecture and Sturmian words", European Journal of Combinatorics, 28 (3): 876–890, doi:10.1016/j...
7 KB (938 words) - 02:19, 12 April 2025