We say that a sequence (xn) n∈ N in [0, 1) has Poissonian pair correlations if lim N→∞ 1
N# 1≤ l≠ m≤ N:‖ xl− xm‖≤ s N= 2 s for every s≥ 0. The aim of this article is twofold …

Years ago Zeev Rudnick defined the $\lambda $-Poisson generic sequences as the infinite
sequences of symbols in a finite alphabet where the number of occurrences of long words in …

Émile Borel defined normality more than 100 years ago to formalize the most basic form of
randomness for real numbers. A number is normal to a given integer base if its expansion in …

We introduce a variant of de Bruijn words that we call perfect necklaces. Fix a finite alphabet.
Recall that a word is a finite sequence of symbols in the alphabet and a circular word, or …

We introduce and study a new complexity function in combinatorics on words, which takes
into account the smallest second occurrence time of a factor of an infinite word. We …

A string attractor is a set of positions in a word such that each distinct factor has an
occurrence crossing a position from the set. This definition comes from the data compression …

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 preference function provides a method to build periodic sequences by specifying a set of
rules that determine which symbols are to be attempted before others, when the sequence is …

We present a measure of string complexity, called I-complexity, computable in linear time
and space. It counts the number of different substrings in a given string. The least complex …

I will show that there exist two binary words (one of length 4 and one of length 6) that play a
special role in many different problems in combinatorics on words. They can therefore be …