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arXiv · 2104.09985

A Separation of $\gamma$ and $b$ via Thue--Morse Words

Hideo Bannai·Mitsuru Funakoshi·Tomohiro I·Dominik Koeppl·Takuya Mieno·Takaaki Nishimoto
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Abstract

We prove that for $n\geq 2$, the size $b(t_n)$ of the smallest bidirectional scheme for the $n$th Thue--Morse word $t_n$ is $n+2$. Since Kutsukake et al. [SPIRE 2020] show that the size $\gamma(t_n)$ of the smallest string attractor for $t_n$ is $4$ for $n \geq 4$, this shows for the first time that there is a separation between the size of the smallest string attractor $\gamma$ and the size of the smallest bidirectional scheme $b$, i.e., there exist string families such that $\gamma = o(b)$.

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Hideo Bannai, Mitsuru Funakoshi, Tomohiro I, Dominik Koeppl, Takuya Mieno, Takaaki Nishimoto. 2021-04-19. A Separation of $\gamma$ and $b$ via Thue--Morse Words. https://arxiv.org/abs/2104.09985

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