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Least Periods of Factors of Infinite Words
(EDP Sciences, 2009)
We show that any positive integer is the least period of a factor of the Thue-Morse word. We also characterize the set of least periods of factors of a Sturmian word. In particular, the corresponding set for the Fibonacci ...
Suffix conjugates for a class of morphic subshifts
(Cambridge University Press, 2015-09)
Let A be a finite alphabet and f: A^* --> A^* be a morphism with an iterative fixed point f^\omega(\alpha), where \alpha{} is in A. Consider the subshift (X, T), where X is the shift orbit closure of f^\omega(\alpha) and ...
Cubefree words with many squares
(Discrete Mathematics and Theoretical Computer Science, 2014-05-13)
We construct infinite cubefree binary words containing exponentially many distinct squares of length n . We also show that for every positive integer n , there is a cubefree binary square of length 2n.
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 ...
For each a > 2 there is an Infinite Binary Word with Critical Exponent a
(The Electronic Journal of Combinatorics, 2008-08-31)
The critical exponent of an infinite word w is the supremum of all rational numbers α such that w contains an α-power. We resolve an open question of Krieger and Shallit by showing that for each α>2 there is an infinite ...
On avoidability of formulas with reversal
(EDP Sciences, 2018-02-13)
While a characterization of unavoidable formulas (without reversal) is well-known, little
is known about the avoidability of formulas with reversal in general. In this article, we characterize the unavoidable formulas ...
Binary Words Containing Infinitely Many Overlaps
(The Electronic Journal of Combinatorics, 2006-09-22)
We characterize the squares occurring in infinite overlap-free binary words and construct various α power-free binary words containing infinitely many overlaps.