User:Inthar/MV3: Difference between revisions
→MV3 Theorem 1: clean up notation for readability |
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=== Lemma 2: Sizes of chunks of any fixed letter form a MOS (except in the case " | === Lemma 2: Sizes of chunks of any fixed letter form a MOS (except in the case "xyzyx") === | ||
TODO: account for case | 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) | Assume the scale word S is not multiperiod. To eliminate XYZYX we manually check all words up to length 5... (todo) | ||
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Now assume len(S) >= 6. | Now assume len(S) >= 6. | ||
WOLOG consider chunks of | WOLOG consider chunks of x. Use q for any occurrence of either y and z. | ||
say you have some intvl class (k steps) with 3 variants in | say you have some intvl class (k steps) with 3 variants in x's and q's: | ||
* S1 = | * S1 = a1x + b1q, represented by the word s1 in the MV3 scale | ||
* S2 = | * S2 = a2x + b2q, word s2 | ||
* S3 + | * S3 = a3x + b3q, word s3 | ||
(si to be chosen later) | (si to be chosen later) | ||
Say that the mos formed by the Ys and Zs is rY sZ, wolog r > s. | Say that the mos formed by the Ys and Zs is rY sZ, wolog r > s. | ||
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First we prove that chunk sizes can't differ by 2 or more. | First we prove that chunk sizes can't differ by 2 or more. | ||
have some length (say that of biggest chunk of | have some length (say that of biggest chunk of x's) word with no q's and >=2 q's. | ||
now y[biggest]z => contradiction bc two kinds of "one q" | now y[biggest]z => contradiction bc two kinds of "one q" | ||