Rank-3 scale theorems: Difference between revisions
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* Assume ''S'' is a 2-step scale. Then ''S'' is ''slope-LQ'' if the slope between any two pair of points (representing a ''k''-mosstep) is one of the two nearest possible slopes (in the set {k/0,...,0/k}) to b/a. | * Assume ''S'' is a 2-step scale. Then ''S'' is ''slope-LQ'' if the slope between any two pair of points (representing a ''k''-mosstep) is one of the two nearest possible slopes (in the set {k/0,...,0/k}) to b/a. | ||
* Say that a 2-step scale ''S'' is ''floor-LQ'' if some mode ''M'' of ''S'' satisfies that γ(''M'') = the graph of floor(b/a*x). | * Say that a 2-step scale ''S'' is ''floor-LQ'' if some mode ''M'' of ''S'' satisfies that γ(''M'') = the graph of floor(b/a*x). | ||
* Say that | * Say that an r-step scale ''S'' is ''LQ'' if any appropriate line in generic position, (a_1, ..., a_r)t + v_0, has intersections with coordinate level planes x_i = k that spell out the scale as you move in the positive t direction. | ||
===== 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. | Assume wlog there are more L's than s's. | ||