並列摘要
For all x ∈ R, define [x] = n where n ∈ Z, n≤x ＜ n+1. For all x ∈ R, define[x]=n where n ∈ Z, n-1＜x≤n. Let α=[(√5)-1]/2. Define the following two-way infinite binary words.(a) G= ...d(subscript -n)d(subscript n+1)...d(subscript -1)d(subscript 0)d(subscript 1)...d(subscript n)d(suscript n+1)..., where the nth letter d(subscript n)=[(n+1)α]-[nα], n ∈ Z.(b) H = ...e(subscript -n)e(subscript n+1)...e(subscript -1)e(subscript 0)e(subscript 1)...e(subscript n)e(subscript n+1)..., where the nth letter e(subscript n) =[(n+1)α]-[nα], n ∈ Z.Hence G and H are called two-way infinite words. In this paper, we will find all square prefixes of G(subscript m) (or H(subscript m)) for each m ∈ Z.
延伸閱讀
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