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Growth rate of binary words avoiding xxxR
(Elsevier, 2016-01)
Abstract
Consider the set of those binary words with no non-empty factors of the form
xxx^R. Du, Mousavi, Schaeffer, and Shallit asked whether this set of words grows
polynomially or exponentially with length. In this ...
Infinite words containing squares at every position
(EDP Sciences, 2010)
Richomme asked the following question: what is the infimum of the real numbers α > 2 such that there exists an infinite word that avoids α-powers but contains arbitrarily large squares beginning at every position? We resolve ...
Multi-dimensional sets recognizable in all abstract numeration systems
(EDP Sciences, 2011)
We prove that the subsets of Nd that are S-recognizable for all abstract numeration systems S are exactly the 1-recognizable sets. This generalizes a result of Lecomte and Rigo in the one-dimensional setting.
The minimal automaton recognizing mN in a linear numeration system
(Integers, 2011-12-02)
We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly connected component ...
Further applications of a power series method for pattern avoidance
(The Electronic Journal of Combinatorics, 2011-06-21)
In combinatorics on words, a word w over an alphabet ∑ is said to avoid a pattern
p over an alphabet ∆ if there is no factor x of w and no non-erasing morphism h
from ∆* to ∑* such that h(p) = x. Bell and Goh have recently ...
Cyclic Complexity of Some Infinite Words and Generalizations
(Integers, 2018-03)
Cassaigne et al. introduced the cyclic complexity function c_x(n), which gives the number of cyclic conjugacy classes of length-n factors of a word x. We study the behavior of this function for the Fibonacci word f and the ...
Automaticity of Primitive Words and Irreducible Polynomials
(Discrete Mathematics and Theoretical Computer Science, 2013)
If L is a language, the automaticity function AL(n) (resp. NL(n)) of L counts the number of states of a smallest deterministic (resp. non-deterministic) finite automaton that accepts a language that agrees with L on all ...
Avoiding approximate repetitions with respect to the longest common subsequence distance
(Mathematical Sciences Publishers, 2015-09-17)
Ochem, Rampersad, and Shallit gave various examples of infinite words avoiding what they called approximate repetitions. An approximate repetition is a factor of the form x x', where x and x' are close to being identical. ...
Abelian complexity of fixed point of morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1
(Integers, 2014-02-20)
We study the combinatorics of vtm, a variant of the Thue-Morse word generated by the non-uniform morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1 starting with 0. This infinite ternary sequence appears a lot in the literature and finds ...
Extremal words in morphic subshifts
(Elsevier, 2014-01-22)
Given an infinite word x over an alphabet A, a letter b occurring in
x, and a total order \sigma on A, we call the smallest word with respect to \sigma
starting with b in the shift orbit closure of x an extremal word of ...