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Discrete Applied Mathematics, ISSN 0166-218X, 12/2016, Volume 214, pp. 63 - 87
We prove that all suffixes of a two-way infinite extension of an irrational characteristic word can be represented as Markov word patterns (MWPs) of type 1 and... 
Irrational characteristic word | Seed word | Adjacent [formula omitted]-word | Markov word pattern | Simple Sturmian word | Adjacent α-word | MATHEMATICS, APPLIED | FACTORIZATION | REPRESENTATION | STURMIAN WORDS | CHARACTERISTIC SEQUENCES | LYNDON WORDS | MORPHISMS | Adjacent alpha-word | INFINITE FIBONACCI WORDS | SUFFIXES | IRRATIONAL NUMBERS | MOMENTS
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 10/2019, Volume 790, pp. 16 - 40
We introduce a variation of the Ziv–Lempel and Crochemore factorizations of words by requiring each factor to be a palindrome. We compute these factorizations... 
Ziv–Lempel factorization | Palindrome | Singular words | m-Bonacci words | Fibonacci word | Crochemore factorization | Episturmian words | Ziv-Lempel factorization | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS | Computer science
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 11/2019, Volume 792, pp. 144 - 153
Minimal forbidden factors are a useful tool for investigating properties of words and languages. Two factorial languages are distinct if and only if they have... 
Circular word | Finite automaton | Minimal forbidden factor | Fibonacci words | Factor automaton | SUFFIX | COMPUTER SCIENCE, THEORY & METHODS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 07/2016, Volume 207, pp. 56 - 66
A word w=w1w2⋯wn is alternating if either w1 w3 ⋯ (when the word is up-down) or w1>w2 w4<⋯ (when the word is down-up). In this paper, we initiate the study of... 
Bijection | Up-down words | Order ideals | Alternating words | Down-up words | Narayana numbers | Fibonacci numbers | Pattern-avoidance | MATHEMATICS, APPLIED | PERMUTATIONS | SUBSEQUENCES | Permutations | Set theory | Equivalence | Mathematical analysis | Formulas (mathematics) | Avoidance
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 04/2015, Volume 21, Issue 1-3, pp. 3 - 11
•The theory of grossone is used to study infinite Fionacci words.•The use of the heptagrid, a tiling of the hyperbolic plane, allows us to illustrate these... 
Hyperbolic plane | Tilings | Fibonacci words | Grossone | INFINITESIMALS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NUMBERS | PHYSICS, FLUIDS & PLASMAS | BLINKING FRACTALS | PHYSICS, MATHEMATICAL | Tools | Nonlinearity | Mathematical models | Tiling | Planes | Computer simulation
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 07/2016, Volume 635, pp. 16 - 34
Richomme, Saari and Zamboni (2011) [39] proved that at every position of a Sturmian word starts an abelian power of exponent k for every k>0. We improve on... 
Abelian period | Critical exponent | Sturmian word | Abelian power | Lagrange constant | ALGEBRAIC-NUMBERS | EPISTURMIAN WORDS | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Exponents | Computation | Analogue | Quotients | Mathematical analysis | Constants | Fibonacci numbers | Repetition | Data Structures and Algorithms | Computer Science
Journal Article
European Journal of Combinatorics, ISSN 0195-6698, 05/2019, Volume 78, pp. 121 - 133
In this paper, first, we introduce two classification criteria of non-isometric words, and characterize every type of non-isometric words. Then, according to... 
MATHEMATICS | INDEX | GENERALIZED FIBONACCI CUBES | GOOD BAD WORDS
Journal Article
Carpathian Mathematical Publications, ISSN 2075-9827, 06/2016, Volume 8, Issue 1, pp. 11 - 15
In this paper we introduce two families of periodic words (FLP-words of type 1 and FLP-words of type 2) that are connected with the Fibonacci words and... 
Fibonacci numbers, Fibonacci word
Journal Article
Acta Mathematica Sinica, English Series, ISSN 1439-8516, 06/2017, Volume 33, Issue 6, pp. 851 - 860
Generalized Fibonacci cube Q(d) (f), introduced by IliAc, Klavzar and Rho, is the graph obtained from the hypercube Q(d) by removing all vertices that contain... 
isometric subgraph | Generalized Fibonacci cube | good word | bad word | MATHEMATICS | MATHEMATICS, APPLIED | GENERALIZED FIBONACCI CUBES | ENUMERATIVE PROPERTIES | INDEX | LUCAS CUBES | Graph theory | Mathematical analysis | Fibonacci numbers | Digits
Journal Article
European Journal of Combinatorics, ISSN 0195-6698, 01/2017, Volume 59, pp. 204 - 214
The generalized Fibonacci cube Qd(f) is the graph obtained from the hypercube Qd by removing all vertices that contain a given binary word f. A word f is... 
MATHEMATICS | INDEX | GENERALIZED FIBONACCI CUBES | LUCAS CUBES | Integers | Algorithms | Cubes | Graphs | Hypercubes | Graph theory | Combinatorial analysis
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2015, Volume 186, Issue 1, pp. 128 - 146
In this paper, we introduce the notion of an (a,b)-rectangle pattern on permutations which is closely related to the notion of successive elements (bonds) in... 
Successions in permutations | Permutations | LEGO | [formula omitted]-box patterns | Mesh patterns | [formula omitted]-rectangle patterns | Words | Distribution | Bond | Fibonacci numbers | [formula omitted]-bond | K-bond | K-box patterns | (a,b)-rectangle patterns | MATHEMATICS, APPLIED | (a, b)-rectangle patterns | k-bond | k-box patterns
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 2011, Volume 412, Issue 8, pp. 876 - 891
Let α = ( a 1 , a 2 , … ) be a sequence (finite or infinite) of integers with a 1 ≥ 0 and a n ≥ 1 , for all n ≥ 2 . Let { a , b } be an alphabet. For n ≥ 1 ,... 
Radix order | Lexicographic order | [formula omitted]-word | α-word | CHARACTERISTIC SEQUENCES | MORPHISMS | COMPUTER SCIENCE, THEORY & METHODS | FIBONACCI WORDS | STURMIAN WORDS | CONJUGACY | IRRATIONAL NUMBERS | alpha-word | Integers | Mathematical analysis | Alphabets | Labels | Mathematical models | Strings | Combinatorial analysis
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 217, pp. 243 - 260
Let α be an irrational number between 0 and 1 with continued fraction expansion [0;a1+1,a2,a3,…], where an≥1 (n≥1). Define a sequence of numbers {qn}n≥−1 by... 
[formula omitted]-representation of numbers | Markov word pattern | Factorization | Singular word | [formula omitted]-word | Characteristic word | α-word | Q-representation of numbers | MATHEMATICS, APPLIED | NUMBERS | REPRESENTATION | STURMIAN WORDS | alpha-word | CHARACTERISTIC SEQUENCES | FIBONACCI WORDS | ALPHA-WORDS
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 10/2017, Volume 696, pp. 1 - 10
Let Fk be the family of the binary words containing the letter 0 exactly k times. Ilić, Klavžar and Rho constructed an infinite subfamily of 2-isometric and... 
s-isometric word | Binary word | Non-isometric word | Isometric word | STRINGS | GENERALIZED FIBONACCI CUBES | COMPUTER SCIENCE, THEORY & METHODS | INDEX | BAD WORDS | LUCAS CUBES | Information science
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 02/2018, Volume 711, Issue 8, pp. 92 - 104
We prove that if a Sturmian word is the image by a morphism of a word which is a fixed point of another morphism, then this latter word is mostly a Sturmian... 
Sturmian words | D0L systems | Standard morphisms | Fibonacci word | Sturmian morphisms | HD0L systems | CONJUGATION | DOL systems | HDOL systems | ITERATED MORPHISMS | COMPUTER SCIENCE, THEORY & METHODS | Computer Science | Discrete Mathematics
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 07/2016, Volume 208, pp. 114 - 122
The initial non-repetitive complexity function of an infinite word x (first introduced by Moothathu) is the function of n that counts the number of distinct... 
Tribonacci word | Squarefree word | Thue–Morse word | Fibonacci word | Initial non-repetitive complexity | Thue-Morse word | MATHEMATICS, APPLIED | Functions (mathematics) | Mathematical analysis | Images | Formulas (mathematics) | Repetition | Counting | Complexity
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 01/2014, Volume 121, Issue 1, pp. 34 - 44
It is a fundamental property of non-letter Lyndon words that they can be expressed as a concatenation of two shorter Lyndon words. This leads to a naive lower... 
Fibonacci word | Lyndon word | Sturmian word | Golden ratio | Central word | Periodicity | MATHEMATICS
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 06/2012, Volume 437, pp. 69 - 81
The studies of 1-Fibonacci word patterns and 0-Fibonacci word patterns were initiated by Turner (1988) [18] and Chuan (1993) [2] respectively. It is known that... 
Seed word | [formula omitted]-Fibonacci word pattern | Two-way infinite Fibonacci word | Label of Fibonacci word | Sturmian morphism | Mechanical word | r-Fibonacci word pattern | CHARACTERISTIC SEQUENCES | PROPERTY | COMPUTER SCIENCE, THEORY & METHODS | SUFFIXES | ALPHA-WORDS
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 11/2019, Volume 795, pp. 301 - 311
Recently the Fibonacci word W on an infinite alphabet was introduced by Zhang et al. (2017) [13] as a fixed point of the morphism... 
Palindrome | Fibonacci word | Lyndon word | Square | LYNDON WORDS | COMPUTER SCIENCE, THEORY & METHODS | SQUARES
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 08/2015, Volume 593, pp. 106 - 116
Let ω be a factor of the Fibonacci sequence F∞=x1x2⋯, then it occurs in the sequence infinitely many times. Let ωp be the p-th occurrence of ω and rp(ω) be the... 
Singular decomposition | Return words | Fibonacci sequence | Singular kernel | Spectrum | LYNDON WORDS | COMPUTER SCIENCE, THEORY & METHODS | STURMIAN WORDS | Kernels | Decomposition | Alphabets | Combinatorial analysis
Journal Article
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