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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.
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 ...
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
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.
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 ...
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)
Extremal Infinite Overlap-Free Binary Words
(The Electronic Journal of Combinatorics, 1998-05-03)
Let t be the infinite fixed point, starting with 1, of the morphism μ:0→01, 1→10. An infinite word over {0,1} is said to be overlap-free if it contains no factor of the form axaxa, where a∈{0,1} and x∈{0,1}∗. We prove that ...
Non-Repetitive Tilings
(The Electronic Journal of Combinatorics, 2002-07-03)
In 1906 Axel Thue showed how to construct an infinite non-repetitive (or square-free) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a two-dimensional ...