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#### There are Ternary Circular Square-Free Words of Length n for n ≥ 18

(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.

#### 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.

#### 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 ...

#### 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

#### 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 ...

#### 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 ...

#### 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 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.