Rank-3 scale theorems: Difference between revisions
No edit summary Tags: Mobile edit Mobile web edit |
No edit summary Tags: Mobile edit Mobile web edit |
||
| Line 37: | Line 37: | ||
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: (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. | ||
Suppose that some k-step comes in 3 "sizes". | |||
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. | 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. | ||