Generator-offset property: Difference between revisions
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Either β′′ = β or β′′ = β′. Assume β′′ = β′. Then γ′′ = γ, and Λ<sub>3</sub> is (λ + 1)γ (μ − 1)γ′. Also assume that the first ''k''-step in Σ is Q. Then we have: | Either β′′ = β or β′′ = β′. Assume β′′ = β′. Then γ′′ = γ, and Λ<sub>3</sub> is (λ + 1)γ (μ − 1)γ′. Also assume that the first ''k''-step in Σ is Q. Then we have: | ||
1 … n | 1 … n | ||
Σ = Q W(Q, R) T | Σ = Q ''W''(Q, R) T | ||
Λ<sub>1</sub> = α … α α′ | Λ<sub>1</sub> = α … α α′ | ||
Λ<sub>2</sub> = β W(β, β′) β′ | Λ<sub>2</sub> = β ''W''(β, β′) β′ | ||
Λ<sub>3</sub> = γ W(γ, γ′) γ | Λ<sub>3</sub> = γ ''W''(γ, γ′) γ | ||
where W = W(''x'', ''y'') is a word in two variables ''x'' and ''y'', of length ''n'' − 2. | where ''W'' = ''W''(''x'', ''y'') is a word in two variables ''x'' and ''y'', of length ''n'' − 2. | ||
===== Case analysis ===== | ===== Case analysis ===== | ||