On the abelian complexity of generalized Thue-Morse sequences
Chen, Jin · Wen, Zhi-Xiong
Original · EN
In this paper, we study the abelian complexity ρₙab(t⁽ᵏ⁾) of generalized Thue-Morse sequences t⁽ᵏ⁾. We obtain the exact value of ρₙab(t⁽ᵏ⁾) for every integer n≥ k. Consequently, ρₙab(t⁽ᵏ⁾) is ultimately periodic with the period k. Moreover, we show that the abelian complexities of a class of infinite sequences are k-automatic.
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