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 ...

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 ...

The authors introduce the notion of crown-like orders and introduce powerful tools for counting the endomorphisms of orders of this type.

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, ...

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 ...

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 ...

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 ...

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 ...

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 ...

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.