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Now showing items 1-10 of 39

#### The metric dimension and metric independence of a graph

(The Charles Babbage Research Centre, 2001)

A vertex x of a graph G resolves two vertices u and v of G if the
distance from x to u does not equal the distance from x to v. A set
S of vertices of G is a resolving set for G if every two distinct vertices
of G are ...

#### 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 ...

#### 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.

#### Unary patterns under permutations

(Elsevier, 2018-06-04)

Thue characterized completely the avoidability of unary patterns. Adding function variables gives a general setting capturing avoidance of powers, avoidance of patterns with palindromes, avoidance of powers under coding, ...

#### 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 ...

#### 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 ...

#### 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 ...

#### A family of formulas with reversal of high avoidability index

(World Scientific, 2017)

We present an infinite family of formulas with reversal whose avoidability index is bounded between 4 and 5, and we show that several members of the family have avoidability index 5. This family is particularly interesting ...

#### 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 ...

#### 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.