Manuel Almeida Silva
Universidade Nova de Lisboa

Abstract: In combinatorics of words, a concatenation of k consecutive equal blocks is called a power of order k. We define an anti-power of order k as a concatenation of k consecutive pairwise distinct blocks of the same length. We show that every infinite word contains powers of any order or anti-powers of any order. That is, the existence of powers or anti-powers is an unavoidable regularity. We will also generalize two combinatorial constructions given by Justin and Pirillo concerning arbitrarily large monochromatic k-powers occurring in infinite words and give a new classe of infinite words that do not allow infinite monochromatic factorizations.

Seminário financiado por Fundos Nacionais através da FCT – Fundação para a Ciência e Tecnologia no âmbito do projeto UID/MAT/04721/2013.