Rank-3 scale theorems: Difference between revisions

Inthar (talk | contribs)
Inthar (talk | contribs)
Line 100: Line 100:
====== PMOS implies AG (except in the case xyxzxyx) (WIP) ======
====== PMOS implies AG (except in the case xyxzxyx) (WIP) ======


====== AG + MV3 implies "ax by bz" (WIP) ======
====== AG + MV3 implies "ax by bz" ======
AG by itself does ''not'' imply "ax by bz"; [[blackdye]] (LSLMLSLMLS) is a counterexample.
AG by itself does ''not'' imply "ax by bz"; [[blackdye]] (LSLMLSLMLS) is a counterexample.


Line 122: Line 122:
* k g1 + (k-1) g2
* k g1 + (k-1) g2
* (k-1) g1 + k g2
* (k-1) g1 + k g2
* (k-1) g1 + (k-1) g2 + g3
* (k-1) g1 + (k-1) g2 + g3.
if a step is an odd number of generators (since the scale size is odd, we can always ensure this by taking octave complements of all the generators). The first two sizes must occur the same number of times.
If a step is an odd number of generators (since the scale size is odd, we can always ensure this by taking octave complements of all the generators). The first two sizes must occur the same number of times.


==== 3-DE implies MV3 (WIP) ====
==== 3-DE implies MV3 (WIP) ====