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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 ...
Avoiding three consecutive blocks of the same size and same sum
(Association of Computing Machinery, 2014-04)
We show that there exists an infinite word over the alphabet {0,1,3,4} containing no three consecutive blocks of the same size and the same sum. This answers an open problem of Pirillo and Varricchio from1994.
There Exist Binary Circular 5/2+ Power Free Words of Every Length
(The Electronic Journal of Combinatorics, 2004-01-23)
We show that there exist binary circular 5/2+ power free words of every length.
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.
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.
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.
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 ...
Attainable lengths for circular binary words avoiding k-powers
(The Belgian Mathematical Society, 2005)
We show that binary circular words of length n avoiding 7/3+ powers exist
for every sufficiently large n. This is not the case for binary circular words
avoiding k+ powers with k < 7/3
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 ...