User:Inthar/MV3: Difference between revisions
No edit summary Tags: Mobile edit Mobile web edit |
No edit summary Tags: Mobile edit Mobile web edit |
||
| Line 76: | Line 76: | ||
=== 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). | 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. | ||
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) | ||
| Line 86: | Line 86: | ||
* in y, η (η = x or z), with gen g2 | * in y, η (η = x or z), with gen g2 | ||
* in z, ζ (ζ = x or y), with gen g3. | * in z, ζ (ζ = x or y), with gen g3. | ||
Suppose no gen chain g_i detempers to a chain of alternating generators. | |||
=== Proof of "ax by bz" (except in case xyxzxyx) === | === Proof of "ax by bz" (except in case xyxzxyx) === | ||