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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 ...
Counting endomorphisms of crown-like orders
(Springer,2002-12)
The authors introduce the notion of crown-like orders and introduce powerful tools for counting the endomorphisms of orders of this type.
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.
A direct proof of a result of Thue
(Utilitas Mathematica,1984)
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 ...
表征除00、11和0101以外的二进制圆形单词的长度
(2020-05-19)
我们精确地表征了除00、11和0101以外没有其他正方形的二进制圆形单词的长度。
n≥18有三元圆形的长度n
(The Electronic Journal of Combinatorics,2002-10-11)
There are circular square-free words of length n on three symbols for n≥18. This proves a conjecture of R. J. Simpson.
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 ...