Avoiding abelian and additive powers in rich words

2024/08/27 by Andrade, Jonathan, Mol, Lucas
#68R15 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL)

paper · doi:10.48550/arxiv.2408.15390

Abstract

This paper concerns the avoidability of abelian and additive powers in infinite rich words. In particular, we construct an infinite additive 5-power-free rich word over \0,1\ and an infinite additive 4-power-free rich word over \0, 1, 2\. The alphabet sizes are as small as possible in both cases, even for abelian powers.

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