Rank-3 scale theorems: Difference between revisions
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# g2 (even) g1 g3 g1 (even) g2 (inverse of #1) = (n/2-1) g1 + (n/2-1) g2 + g3 | # g2 (even) g1 g3 g1 (even) g2 (inverse of #1) = (n/2-1) g1 + (n/2-1) g2 + g3 | ||
# g1 (odd) g1 g3 g1 (odd) g1 (inverse of #2) = n/2 g1 + (n/2-2) g2 + g3. | # g1 (odd) g1 g3 g1 (odd) g1 (inverse of #2) = n/2 g1 + (n/2-2) g2 + g3. | ||
Choose a tuning where g1 | Choose a tuning where g1 = 1/2*g0 + ε, g2 = 1/2*g0 - ε. We have 4 distinct sizes for n/2-steps, a contradiction to MV3: | ||
(1) #1, #2 and #3 are clearly distinct. | (1) #1, #2 and #3 are clearly distinct. | ||