Rank-3 scale theorems: Difference between revisions

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 where u_L and u_s are the larger and smaller B_0-steps of w_X.
-Eliminating Y from w, w_Y is a mos (with letters X and Z). Consider chunks of Z bounded by X's, of sizes c and c+1. Within any contiguous subword with A_0-many X's, the number of Z's will be within [K, K+c+1], for some constant K:
+Plan: v_2 and v_3 are sizes that are problematic when they occur together.
- X...XZZZ...Z (suffix = at most c+1 Z's)
-[Get two subwords s_1, s_2 in w_Y with A_0-many X's and two numbers of Z's. These should be Y-eliminated versions of subwords t_1, t_2 in w, with two numbers of Y's by the fact that w_X is a mos. Get the right number of Y's to have a B_0-step, by using w_Z]
 ====== PMOS implies AG (except in the case xyxzxyx) (WIP) ======