User:Inthar/MV3: Difference between revisions
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=== Lemma 2: Sizes of chunks of any fixed letter form a MOS (except in the case "XYZYX") === | === Lemma 2: Sizes of chunks of any fixed letter form a MOS (except in the case "XYZYX") === | ||
TODO: account for case XYZYX. | TODO: account for case XYZYX. | ||
Assume the scale word S is not multiperiod. To eliminate XYZYX we manually check all words up to length 5... (todo) | |||
Now assume len(S) >= 6. | |||
WOLOG consider chunks of X. Use Q for both Y and Z. | WOLOG consider chunks of X. Use Q for both Y and Z. | ||
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''To be continued...'' | ''To be continued...'' | ||
=== Finishing the proof === | === Finishing the proof === | ||
We now prove that except in the case XYXZXYX, if the scale is pairwise well-formed, the scale is generated by alternating generators. | We now prove that except in the case XYXZXYX, if the scale is pairwise well-formed, the scale is generated by alternating generators. | ||