Abstract

Let Fk be the family of the binary words containing exactly k 0s. Ilić, Klavžar and Rho constructed an infinite subfamily of 2-isometric but not 3-isometric words among F2. Wei, Yang and Wang further found there are 2-isometric but not 3-isometric words among Fk for all k∈{2,5,6} and k≥8, and they conjectured that F1, F3, F4 and F7 are the only families in which there are not 2-isometric but not 3-isometric words. In the present paper, we show that this conjecture is true, and find all the 2-isometric words among F5 and F6.

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