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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 ...
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 ...
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 ...
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 ...