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Fibonacci word

In mathematics, more specifically in combinatorics on words, a Fibonacci word is a specific sequence of binary digits (or symbols from any two-letter alphabet) formed by repeated concatenation in the same way that the Fibonacci numbers are formed by repeated addition.

Applications, Other properties & Closed-form expression for individual digits

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Other properties

PalindromePalindromic densityBalanced sequenceFactorsHamming weights
14 related topics

Applications

QuasicrystalsCrystal growth
2 related topics

Closed-form expression for individual digits

Golden ratioFloor function
2 related topics

Definition

OEIS
1 related topics

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Overview

Definition

  • OEIS On-Line Encyclopedia of Integer Sequences

Closed-form expression for individual digits

Discussion

Other properties

Applications

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Map overview Semantic statistics

Fibonacci word

Nodes37
Edges36
Triples134
Avg. degree1.95
Density0.054054
Components1

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Fibonacci word

Top relations

related to References · 84
Fibonacci word → Adamczewski, Aldo, Algebraic Combinatorics, Allouche, An, Application, Applications, Automatic Sequences, Baribeau, Berstel, Berthé, Bibcode, Boris, Bugeaud, C3, Cambridge, Cambridge University Press, Clark, Combinatorics, Conference
related to Other properties · 19
Fibonacci word → A000201, A001950, Although, Being, Example, Fibonacci, Hamming, If, In, It, Lower Wythoff, OEIS, Sturmian, Suppressing, Take, The, There, Upper Wythoff, Zeckendorf
related to Closed-form expression for individual digits · 6
Fibonacci word → A003849, As, Fibonacci, OEIS, See, The
related to External links · 6
Fibonacci word → Eric, First, MathWorldFibonacci Word, Rabbit Sequence, Ron Knott's, YouTube
related to Substitution rules · 6
Fibonacci word → Alternatively, Another, Fibonacci, In, Sn, Then
is a · 5
Fibonacci word → balanced sequence, limit S, morphic word, specific sequence of binary digits, standard word generated by the directive sequence
related to Definition · 4
Fibonacci word → Fibonacci, Let, Now, The
has application · 2
Fibonacci word → Crystal, Fibonacci

Important terminology Word statistics

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Important terminology

fibonacci word infinite sequence displaystyle doi words number 10 two isbn letters applications also mathematics varphi numbers length digits concatenation

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Fibonacci wordis aspecific sequence of binary digits0.90text
Fibonacci wordis alimit S0.90text
Fibonacci wordis abalanced sequence0.90text
Fibonacci wordis astandard word generated by the directive sequence0.90text
Fibonacci wordis amorphic word0.90text
quasicrystalsinstance ofApplicationsFibonacci based constructions are currently used to model physical systems with aperiodic order0.80text
and in this context the Fibonacci word is also called the Fibonacci quasicrystalinstance ofApplicationsFibonacci based constructions are currently used to model physical systems with aperiodic order0.80text
Fibonacci wordhas applicationFibonacci0.60section
Fibonacci wordhas applicationCrystal0.60section
Fibonacci wordrelated to Closed-form expression for individual digitsThe0.60section
Fibonacci wordrelated to Closed-form expression for individual digitsA0038490.60section
Fibonacci wordrelated to Closed-form expression for individual digitsOEIS0.60section

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