Generator-offset property: Difference between revisions
m →Proof |
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We can assume that the first k-step in Σ is Q: | We can assume that the first k-step in Σ is Q: | ||
1 … | 1 … n | ||
Σ = Q … | Σ = Q … T | ||
Λ<sub>1</sub> = α … | Λ<sub>1</sub> = α … α α’ | ||
Λ<sub>2</sub> = β ( | Λ<sub>2</sub> = β W(β, β’) β’ | ||
Λ<sub>3</sub> = γ ( | Λ<sub>3</sub> = γ W(γ, Γ’) γ | ||
where W is a word in two letters of length n-2. | |||
Since, by our assumption, Λ<sub>3</sub> has two γ’s in a row, Λ<sub>3</sub> must have more γ than γ’, so μ − 1 < n/2. Since Λ<sub>3</sub> is a mos, μ − 1 ≥ 1. So we have 2 ≤ μ ≤ ceil(n/2). | Since, by our assumption, Λ<sub>3</sub> has two γ’s in a row, Λ<sub>3</sub> must have more γ than γ’, so μ − 1 < n/2. Since Λ<sub>3</sub> is a mos, μ − 1 ≥ 1. So we have 2 ≤ μ ≤ ceil(n/2). | ||