Generator-offset property: Difference between revisions
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(In the following, chunk of Λ<sub>2</sub> means chunk of β, and chunk of Λ<sub>3</sub> means chunk of γ.) | (In the following, chunk of Λ<sub>2</sub> means chunk of β, and chunk of Λ<sub>3</sub> means chunk of γ.) | ||
====== Case 3.1 ====== | ====== Case 3.1 ====== | ||
(x, y) = (floor(n/μ), 2*floor(n/μ) − 1) | (x, y) = (floor(n/μ), 2*floor(n/μ) − 1). | ||
Since y − x = floor(n/μ) − 1 and floor(n/μ) ≥ 2, we have: x = floor(n/μ) = 2 and y − x = 1; hence y = 2*floor(n/μ) − 1 = 3. The chunk in Λ<sub>3</sub> whose size is 3 is made from two chunks in Λ<sub>2</sub> of size 1. (So Λ<sub>2</sub> has chunks of size 1 and 2, and Λ<sub>3</sub> has chunks of size 2 and 3.) | Since y − x = floor(n/μ) − 1 and floor(n/μ) ≥ 2, we have: x = floor(n/μ) = 2 and y − x = 1; hence y = 2*floor(n/μ) − 1 = 3. The chunk in Λ<sub>3</sub> whose size is 3 is made from two chunks in Λ<sub>2</sub> of size 1. (So Λ<sub>2</sub> has chunks of size 1 and 2, and Λ<sub>3</sub> has chunks of size 2 and 3.) | ||