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Avoidability index for binary patterns with reversal
(2017)
For every pattern p over the alphabet {x,x^R,y,y^R}, we specify the least k such that p is k-avoidable.
Binary Words Avoiding xxRx and Strongly Unimodal Sequences
(2015-09-14)
In previous work, Currie and Rampersad showed that the growth of the number
of binary words avoiding the pattern xxxR was intermediate between polynomial and
exponential. We now show that the same result holds for the ...
Square-free Words with Square-free Self-shuffles
(The Electronic Journal of Combinatorics, 2014-01-12)
We answer a question of Harju: For every n ≥ 3 there is a square-free ternary word of length n with a square-free self-shuffle.
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 ...
A family of formulas with reversal of high avoidability index
(World Scientific, 2017)
We present an infinite family of formulas with reversal whose avoidability index is bounded between 4 and 5, and we show that several members of the family have avoidability index 5. This family is particularly interesting ...
Characterization of the lengths of binary circular words containing no squares other than 00, 11, and 0101
(2020-05-19)
We characterize exactly the lengths of binary circular words containing no squares other than 00, 11, and 0101.
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 ...
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 ...
Unary patterns under permutations
(Elsevier, 2018-06-04)
Thue characterized completely the avoidability of unary patterns. Adding function variables gives a general setting capturing avoidance of powers, avoidance of patterns with palindromes, avoidance of powers under coding, ...
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 ...