Rank-3 scale theorems: Difference between revisions

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 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) Prve that F(x) describes a mos. This is equivalent to having the line y = b/a*x start at the origin and cross grid lines in x and y coordinates. Every time this line crosses a gridline y = (integer), we write down an s step. Every time it crosses a gridline x = integer, we write down an L. We want to show that this sequence of gridline crossings forms a MOS.
+M_b <= F: Prove that F(x) describes a mos. Two possibilities, for each k from 0 to a-1: (a) F(k + 1) = F(k) or (b) F(k + 1) = F(k) + 1. (b) happens b times, and (a) happens a-b times.
 Suppose that some k-step comes in 3 "sizes".