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Now showing items 1-10 of 27

#### 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 ...

#### 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 ...

#### 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 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

#### 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.

#### 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 ...

#### Combinatorics and Algorithmics of Strings

(Dagstuhl Publishing, 2014-03-09)

Strings (aka sequences or words) form the most basic and natural data structure. They occur whenever information is electronically transmitted (as bit streams), when natural language text is spoken or written down (as words ...