Rank-3 scale theorems: Difference between revisions
→AG implies "ax by bz": Blackdye (LSLMLSLMLS) is a counterexample; it's an example of how the tacit assumption that the generator's size in scale steps is always coprime to the scale size can fail. |
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''The following are equivalent for a non-multiperiod scale word S with steps x, y, z:'' | ''The following are equivalent for a non-multiperiod scale word S with steps x, y, z:'' | ||
# ''S is MV3 for all possible choices of step ratio x:y:z.'' | # ''S is MV3 for all possible choices of step ratio x:y:z.'' | ||
# ''(a) S is PMOS, or (b) S is of the form x'y'z'y'x' or its repetitions, or (c) S has signature nx ny nz, n ≥ 2.'' | # ''(a) S is PMOS, or (b) S is of the form x'y'z'y'x' or its repetitions, or (c) S has signature nx ny nz, n ≥ 2 (and is not a repetition of 1x 1y 1z).'' | ||
# ''S is AG, or S is of the form | # ''Either S is AG and is of the form ax by bz, or S is of the form x'y'x'z'x'y'x' or its repetitions.'' | ||
====== MV3 implies LQ except in the case "xyzyx" (WIP) ====== | ====== MV3 implies LQ except in the case "xyzyx" (WIP) ====== | ||