Rank-3 scale theorems: Difference between revisions
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===== MV2 is equivalent to floor-LQ in 2-step scales (WIP) ===== | ===== MV2 is equivalent to floor-LQ in 2-step scales (WIP) ===== | ||
Assume wlog there are more L's than s's. | |||
MV2 => floor-LQ: Take the graph of the brightest mode of the mos, M_b(x) (right = L, up = s). We claim that this is the required graph of F(x) = floor(b/a*x). | |||
M_b <= F: (bc it's the brightest mode) If brightest(n_0) > floor then I could push that part to the end, which will make it brighter? | |||
M_b >= F: (bc it's a mos) Suppose there is an x-value x_0 where M_b(x_0) < F(x_0). Let m = min(n_0, n-n_0), n = scale size. Then find three different m-mossteps by taking one interval before n_0, one interval containing n_0 and one interval after n_0. | |||
floor-LQ => MV2: | floor-LQ => MV2: | ||