User:Inthar/MV3: Difference between revisions

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=== Lemma 2: Sizes of chunks of any fixed letter form a MOS ===

WOLOG consider chunks of X. Use Q for both Y and Z.

~~First we prove that chunk sizes can't differ by 2 or more.~~

say you have some intvl class (k steps) with 3 variants in X's and Q's:

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By manually eliminating finitely many cases, we can assume that the scale is at least 5 notes and we have at least three Qs.

have some length (say that of ~~max~~ chunk) word with no q's~~,one q~~ and 2 q's.

First we prove that chunk sizes can't differ by 2 or more.

have some length (say that of biggest chunk of X's) word with no q's and >=2 q's.

now y[~~Max~~]z => contradiction bc two kinds of "one q"

now y[biggest]z => contradiction bc two kinds of "one q"

so some non ~~Max~~ chunk has to have y[chunk]z (or z...y)

so some non biggest chunk has to have y[chunk]z (or z...y)

then by using size of [y[non-~~max~~ chunk]z] you get a contradiction bc you can scoot to get an x (since consecutive q's cant happen if there are consecutive x's)

then by using size of [y[non-biggest chunk]z] you get a contradiction bc you can scoot to get an x (since consecutive q's cant happen if there are consecutive x's)

u get [xyxxx...x]z, x[yxxxx...xz]x, y[x...xz], and all x's from the max chunk

@@ Line 49: / Line 49: @@
 === Lemma 2: Sizes of chunks of any fixed letter form a MOS ===
 WOLOG consider chunks of X. Use Q for both Y and Z.
-First we prove that chunk sizes can't differ by 2 or more.
 say you have some intvl class (k steps) with 3 variants in X's and Q's:
@@ Line 63: / Line 61: @@
 By manually eliminating finitely many cases, we can assume that the scale is at least 5 notes and we have at least three Qs.
-have some length (say that of max chunk) word with no q's,one q and 2 q's.
+First we prove that chunk sizes can't differ by 2 or more.
+have some length (say that of biggest chunk of X's) word with no q's and >=2 q's.
-now y[Max]z => contradiction bc two kinds of "one q"
+now y[biggest]z => contradiction bc two kinds of "one q"
-so some non Max chunk has to have y[chunk]z (or z...y)
+so some non biggest chunk has to have y[chunk]z (or z...y)
-then by using size of [y[non-max chunk]z]  you get a contradiction bc you can scoot to get an x (since consecutive q's cant happen if there are consecutive x's)
+then by using size of [y[non-biggest chunk]z] you get a contradiction bc you can scoot to get an x (since consecutive q's cant happen if there are consecutive x's)
 u get [xyxxx...x]z, x[yxxxx...xz]x, y[x...xz], and all x's from the max chunk