We survey known results and open problems in abelian combinatorics on words. Abelian
combinatorics on words is the extension to the commutative setting of the classical theory of …

Random substitutions are a natural generalisation of their classical 'deterministic'counterpart
, whereby at every step of iterating the substitution, instead of replacing a letter with a …

We study the avoidance of Abelian powers of words and consider three reasonable
generalizations of the notion of Abelian power to fractional powers. Our main goal is to find …

In 1961, Paul Erdös posed the question whether abelian squares can be avoided in
arbitrarily long words over a finite alphabet. An abelian square is a non-empty word uv …

The Number of Ternary Words Avoiding Abelian Cubes Grows Exponentially Page 1 23 11
Article 04.2.7 Journal of Integer Sequences, Vol. 7 (2004), 2 3 6 1 47 The Number of …

This collaborative volume aims at presenting and developing recent trends at the interface
between the study of sequences, groups, and number theory, as the title may suggest. It is …

A great deal is known about words avoiding powers. The simplest case occurs with a binary
alphabet. Since the time of Thue [14], it has been known that there are infinite sequences …

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 …

We study abelian repetitions in partial words, or sequences that may contain some unknown
positions or holes. First, we look at the avoidance of abelian pth powers in infinite partial …

We study a new notion of cyclic avoidance of abelian powers. A finite word w avoids abelian
N-powers cyclically if for each abelian N-power of period m occurring in the infinite word w …