Contents
1 Introduction
2 Preliminaries
3 Abelian complexity
3.1 Abelian complexity and periodicity
3.2 Abelian complexity of some families of words
3.3 Abelian pattern complexity
4 Abelian repetitions
4.1 Abelian complexity and abelian powers
4.2 Abelian critical exponent
4.3 Abelian square factors
4.4 Abelian antipowers
5 Abelian avoidability
5.1 Avoidability of abelian powers
5.2 Avoiding fractional abelian repetitions and other generalizations of abelian powers
5.3 Abelian pattern avoidance
6 Abelian periods and borders
6.1 Abelian versions of classical periodicity theorems
6.2 Abelian primitive words
6.3 Abelian borders
7 Abelian properties of Sturmian words
7.1 Abelian powers in Sturmian words
7.2 Abelian critical exponent of Sturmian words
7.3 Abelian periods of factors of Sturmian words
7.4 Abelian returns
7.5 Minimal abelian squares
8 Modifications of abelian equivalence
8.1 k-abelian equivalence
8.2 Weak abelian equivalence
8.3 k-binomial equivalence
8.4 Additive powers
9 Miscellanea
9.1 Abelian subshifts
9.2 Rich words and abelian equivalence
9.3 Abelian saturated words