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

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 ...

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 ...

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.

We classify all 3 letter patterns that are avoidable in the abelian sense. A short list of four letter patterns for which abelian avoidance is undecided is given. Using a generalization of Zimin words we deduce some ...

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 ...

Large context problems (LCP) are useful in teaching the history of science. In this article we consider the brachistochrone problem in a context stretching from Euclid through the Bernoullis. We highlight a variety of ...

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 ...

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

Abstract Consider the set of those binary words with no non-empty factors of the form xxx^R. Du, Mousavi, Schaeffer, and Shallit asked whether this set of words grows polynomially or exponentially with length. In this ...