2020/02/28 by Medková, Kateřina, Pelantová, Edita, Vandomme, Élise
#68R15 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2002.12593
The non-repetitive complexity nrC\bf u and the initial non-repetitive complexity inrC\bf u are functions which reflect the structure of the infinite word \bf u with respect to the repetitions of factors of a given length. We determine nrC\bf u for the Arnoux-Rauzy words and inrC\bf u for the standard Arnoux-Rauzy words. Our main tools are S-adic representation of Arnoux-Rauzy words and description of return words to their factors. The formulas we obtain are then used to evaluate nrC\bf u and inrC\bf u for the d-bonacci word.