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 …

Automatic sequences are sequences over a finite alphabet generated by a finite-state
machine. This book presents a novel viewpoint on automatic sequences, and more …

String matching is one of the oldest algorithmic techniques, yet still one of the most
pervasive in computer science. The past 20 years have seen technological leaps in …

Abstract A string S [1, n] is a power (or tandem repeat) of order k and period n/k if it can be
decomposed into k consecutive equal-length blocks of letters. Powers and periods are …

We determine asymptotic growth rates for lengths of monochromatic arithmetic progressions
in certain automatic sequences. In particular, we look at (one-sided) fixed points of …

A k-antipower (for k ≥ 2) is a concatenation of k pairwise distinct words of the same length.
The study of antipower factors of a word was initiated by Fici et al.(ICALP 2016) and first …

Abstract A string S [1, n] is a power (or repetition or tandem repeat) of order k and period n/k,
if it can be decomposed into k consecutive identical blocks of length n/k. Powers and periods …

Recently, Fici, Restivo, Silva, and Zamboni defined a $ k $-anti-power to be a word of the
form $ w_1w_2\cdots w_k $, where $ w_1, w_2,\ldots, w_k $ are distinct words of the same …

An abelian antipower of order k (or simply an abelian k-antipower) is a concatenation of k
consecutive words of the same length having pairwise distinct Parikh vectors. This definition …

The definition of antipower introduced by Fici et al.(ICALP 2016) captures the notion of being
the opposite of a power: a sequence of k pairwise distinct blocks of the same length …