In mathematics, a Sturmian word (Sturmian sequence or billiard sequence), named after Jacques Charles François Sturm, is a certain kind of infinitely...

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...

In mathematics, a Sturmian sequence may refer to: A Sturmian word: a sequence with minimal complexity function A sequence used to determine the number...

another name for eigenvector of a matrix Characteristic word, a subclass of Sturmian word Euler characteristic, a topological invariant Method of characteristics...

"compact variant" It is conjectured that the Fibonacci word fractal appears for every sturmian word for which the slope, written in continued fraction expansion...

different irrational number. Beatty sequences can also be used to generate Sturmian words. Any irrational number r {\displaystyle r} that is greater than one...

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...

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...

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...

the Lyndon words. Lexicographically minimal string rotation Morphic word Sturmian word Necklace (combinatorics) Lyndon (1954). Shirshov (1953). Berstel &...

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...

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...

al. (2004) Synchronisation of a resonant tunneling diode oscillators Sturmian word Arnol'd, V.I. (1961). "Small denominators. I. Mapping the circle onto...

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...

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...

Chiara; Mignosi, Filippo; Shallit, Jeffrey; Venturini, Ilaria (2004), "Sturmian graphs and a conjecture of Moser", in Calude, Cristian S.; Calude, Elena;...

periodic (meaning periodic after some nonperiodic initial segment). All Sturmian words are uniformly recurrent. Lothaire (2011) p. 30 Allouche & Shallit...

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...

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)...