Generator-offset property: Difference between revisions
m →Case analysis: Using a variable instead of "same" |
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(The lower bound is reached if Λ<sub>3</sub> has chunks of sizes floor(''n''/μ) − 1 and floor(''n''/μ), and the upper bound is reached if Λ<sub>3</sub> has chunks of sizes floor(''n''/μ) and ceil(''n''/μ)). | (The lower bound is reached if Λ<sub>3</sub> has chunks of sizes floor(''n''/μ) − 1 and floor(''n''/μ), and the upper bound is reached if Λ<sub>3</sub> has chunks of sizes floor(''n''/μ) and ceil(''n''/μ)). | ||
The difference between the chunk sizes is ''y'' − ''x'', which must be 0 or 1, since Λ<sub>3</sub> is a mos. We thus have the following subcases: (In the following, chunk of Λ<sub>2</sub> means chunk of β, and chunk of Λ<sub>3</sub> means chunk of γ.) | The difference between the chunk sizes of Λ<sub>3</sub> is ''y'' − ''x'', which must be 0 or 1, since Λ<sub>3</sub> is a mos. We thus have the following subcases: (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:''' (''x'', ''y'') = (floor(''n''/μ), 2*floor(''n''/μ) − 1). | '''Case 3.1:''' (''x'', ''y'') = (floor(''n''/μ), 2*floor(''n''/μ) − 1). | ||