User:Inthar/MV3: Difference between revisions
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No edit summary Tags: Mobile edit Mobile web edit |
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=== Proof of the alternating-gens (AG) property (except in the case xyxzxyx) === | === Proof of the alternating-gens (AG) property (except in the case xyxzxyx) === | ||
We now prove that except in the case xyxzxyx, if the scale is pairwise well-formed, the scale is generated by two chains of generators, either both of size ''m'' or one with size ''m'' and one of size ''m-1'' (AG) Equivalently, the scale can be built by stacking alternating generators, either g1 g2 ... g1 g2 g1 g3 or g1 g2 ... g1 g2 g3. | We now prove that except in the case xyxzxyx, if the scale is pairwise well-formed, the scale is generated by two chains of generators, either both of size ''m'' or one with size ''m'' and one of size ''m-1'' (AG) Equivalently, the scale can be built by stacking alternating generators, resulting in a circle of the form either g1 g2 ... g1 g2 g1 g3 or g1 g2 ... g1 g2 g3. | ||
To eliminate xyxzxyx we manually check all words up to length 7... (todo) | To eliminate xyxzxyx we manually check all words up to length 7... (todo) | ||