A Separation of γ and b via Thue–Morse Words

04/19/2021

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by   Hideo Bannai, et al.

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