An extended special factor of a word x is a factor of x whose longest infix can be extended by
at least two distinct letters to the left or to the right and still occur in x. It is called extended …

Given a finite alphabet Σ and a right-infinite word w over Σ, we define the Lie complexity
function L w: N→ N, whose value at n is the number of conjugacy classes (under cyclic shift) …

The notion of\emph {string attractor} has recently been introduced in [Prezza, 2017] and
studied in [Kempa and Prezza, 2018] to provide a unifying framework for known dictionary …

Inspired by questions raised by Lejeune, we study the relationships between the k and (k+
1)-binomial complexities of an infinite word; as well as the link with the usual factor …

Two words are k-binomially equivalent if each subword of length at most k occurs the same
number of times in both words. The k-binomial complexity of an infinite word is a counting …

In this paper we give a broad unified framework via group actions for constructing complexity
functions of infinite words $ x= x_0x_1x_2\cdots\in\mathbb {A}^{\mathbb {N}} $ with values in …

In combinatorics on words, the well-studied factor complexity function $\rho_ {\bf x} $ of a
sequence ${\bf x} $ over a finite alphabet counts, for any nonnegative integer $ n $, the …

Given a finite non-empty set A, let A+ denote the free semigroup generated by A consisting
of all finite words u 1 u 2⋯ un with ui∈ A. A word u∈ A+ is said to be closed if either u∈ A or …

An abelian square is the concatenation of two words that are anagrams of one another. A
word of length n can contain at most Θ (n 2) distinct factors, and there exist words of length n …

In a recent paper, Jason P. Bell and Jeffrey Shallit introduced the notion of Lie complexity
and proved that the Lie complexity function of an automatic sequence is automatic. In this …