Avoiding squares and overlaps over the natural numbers

  title={Avoiding squares and overlaps over the natural numbers},
  author={Mathieu Guay-Paquet and Jeffrey Shallit},
  journal={Discret. Math.},

Tables from this paper

Avoiding fractional powers over the natural numbers
An automated procedure for proving a/b$-power-freeness for morphisms of a certain form is developed, both for explicit and symbolic rational numbers $a/b$, and a connection to words on a finite alphabet is established.
Avoiding 5/4-Powers on the Alphabet of Nonnegative Integers
The structure of the lexicographically least word avoiding $5/4$-powers on the alphabet of nonnegative integers is identified and it is proved that the sequence of letters is $6$-regular with rank $188$.
Profinite automata
Substitution shifts generated by $p$-adic integer sequences
We set the stage for studying some substitution shifts defined on an infinite alphabet. We consider sequences of p-adic integers that project modulo p to a p-automatic sequence for every α ≥ 0.
Decision Algorithms for Fibonacci-Automatic Words, with Applications to Pattern Avoidance
There exists an aperiodic infinite binary word avoiding the pattern x x x^R, which is the first avoidability result concerning a nonuniform morphism proven purely mechanically.
Mathematisches Forschungsinstitut Oberwolfach Mini-workshop: Combinatorics on Words
The area of combinatorics on words is concerned with properties of sequences of symbols. It is characteristic to the field that questions arise from various mathematical problems, and hence, many
Developments in Language Theory: 24th International Conference, DLT 2020, Tampa, FL, USA, May 11–15, 2020, Proceedings
It is proved that SP (A) and SP (B) are freely generated in their respective natural varieties of algebras V and V ′, and that the equational theory of V ‹ is decidable.
Non-repetitive complexity of infinite words
The non-repetitive complexity function of an infinite word x (first defined by Moothathu) is the function of n that counts the number of distinct factors of length n that appear at the beginning of x


The On-Line Encyclopedia of Integer Sequences
  • N. Sloane
  • Computer Science
    Electron. J. Comb.
  • 1994
The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.
Axel Thue''s papers on repetitions in words: a translation. In: Publications du LaCIM, vol. 20. U
3 Thue's Second Paper : On the relative position of equal parts in certain sequences of symbols 17 3.1 Introductory Remarks Introduction In a series of four papers which appeared during the period
Automatic sequences. Theory, applications, generalizations
What do you do to start reading automatic sequences theory applications generalizations? Searching the book that you love to read first or find an interesting book that will make you want to read?
The Towers of Hanoi and Binary Numerals
  • M. Er
  • Computer Science
  • 1985
Abstract An interesting relation between the Towers of Hanoi and the binary numerals is proved; that is, the disc to be moved in step x is precisely the position of the rightmost 1 in the binary
The Ring of k-Regular Sequences
The automatic sequence is the central concept at the intersection of formal language theory and number theory, and has been extensively studied by Christol, Kamae, Mendes France and Rauzy, and other writers.
The ring of k-regular sequences, II
Substitution dynamical systems on infinite alphabets
Nous etudions quelques exemples de substitutions sur des alphabets infinis, et jetons les bases d'une theorie generale des systemes dynamiques associes. En particulier la substitution "de l'ivrogne"
Propriétés arithmétiques des substitutions et automates infinis
L'objet de ce travail est d'etudier les proprietes arithmetiques et statistiques des mots infinis et des suites de nombres entiers engendres par des substitutions sur un alphabet infini ou par des
Sur la complexité de mots infinis engendrés par des $q$-automates dénombrables
On etudie, dans cet article, les proprietes combinatoires de mots engendres a l'aide de q-automates deterministes denombrables de degre borne, ou de maniere equivalente, engendres par des
Backtrack Programming
A widely used method of efftcient search is examined in detail and its scope and methods are formulated in their full generality.