We study the threshold between avoidable and unavoidable repetitions in infinite balanced
sequences over finite alphabets. The conjecture stated by Rampersad, Shallit and …

We study the properties of the ternary infinite wordp= 012102101021012101021012⋯, that
is, the fixed point of the map h: 0→ 01, 1→ 21, 2→ 0. We determine its factor complexity …

We discuss the use of negative bases in automatic sequences. Recently the theorem-prover
Walnut has been extended to allow the use of base (—k) to express variables, thus …

We revisit the topic of power-free morphisms, focusing on the properties of the class of
complementary morphisms. Such morphisms are defined over a 2-letter alphabet, and map …

We introduce the notion of frequency-constrained substring complexity. For any finite string,
it counts the distinct substrings of the string per length and frequency class. For a string x of …

We study aperiodic balanced sequences over finite alphabets. A sequence vv of this type is
fully characterised by a Sturmian sequence uu and two constant gap sequences yy and …

We study cube-free words over arbitrary non-unary finite alphabets and prove the following
structural property: for every pair (u, v) of d-ary cube-free words, if u can be infinitely …

In combinatorics on words, repetition thresholds are the numbers separating avoidable and
unavoidable repetitions of a given type in a given class of words. For example, the meaning …

We consider sets of factors that can be avoided in square-free words on two-generator free
groups. The elements of the group are presented in terms of {0, 1, 2, 3} such that 0 and 2 …

Abstract In 1985, Restivo and Salemi presented a list of five problems concerning power free
languages. Problem 4 states: Given α-power-free words u and v, decide whether there is a …