In late 2019 and early 2020, governments around the world closed educational institutions due to the COVID-19 pandemic. A similar response occurred in Canada and resulted in a sudden pivot by teachers from classroom-based ...

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 ...

In combinatorics on words, a word w over an alphabet ∑ is said to avoid a pattern p over an alphabet ∆ if there is no factor x of w and no non-erasing morphism h from ∆* to ∑* such that h(p) = x. Bell and Goh have recently ...

Over the past decade we have focused on two interrelated topics within Mesolithic burial studies, the relationship between burial number and burial date, and the chronology of Mesolithic sites with burials. Related to this ...

Let A be a finite alphabet and f: A^* --> A^* be a morphism with an iterative fixed point f^\omega(\alpha), where \alpha{} is in A. Consider the subshift (X, T), where X is the shift orbit closure of f^\omega(\alpha) and ...

Motivated by a conjecture of Frid, Puzynina, and Zamboni, we investigate infinite words with the property that for infinitely many n, every length-n factor is a product of two palindromes. We show that every Sturmian word ...

We construct infinite cubefree binary words containing exponentially many distinct squares of length n . We also show that for every positive integer n , there is a cubefree binary square of length 2n.

The study of combinatorics on words dates back at least to the beginning of the 20th century and the work of Axel Thue. Thue was the first to give an example of an infinite word over a three letter alphabet that contains ...

Ochem, Rampersad, and Shallit gave various examples of infinite words avoiding what they called approximate repetitions. An approximate repetition is a factor of the form x x', where x and x' are close to being identical. ...

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