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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 \(\{\texttt {0},\texttt {1}\}\) and an infinite additive 4-power-free rich word over \(\{\texttt {0},\texttt {1},\texttt {2}\}\) . The alphabet sizes are as small as possible in both cases, even for abelian powers.

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Avoiding Abelian and Additive Powers in Rich Words

  • 会议论文

  • 发表日期：

    2025年

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  • Jonathan Andrade,
  • Lucas Mol

摘要

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 \(\{\texttt {0},\texttt {1}\}\) and an infinite additive 4-power-free rich word over \(\{\texttt {0},\texttt {1},\texttt {2}\}\) . The alphabet sizes are as small as possible in both cases, even for abelian powers.