Generator-offset property: Difference between revisions

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# S = aX bY bZ is obtained from the (single-period) mos aX 2bW by replacing all the W's successively with alternating Y's and Z's (or alternating Z's and Y's for the other chirality).

# The two alternants differ by replacing one Y with a Z.

# ''S'' has the property that the following operations result in a mos: setting L = M, and setting M = s.

# ''S'' has the property that the following operations result in a mos: setting L = M, setting L = s, and setting M = s.

In particular, odd GO scales always satisfy these properties (see Proposition 2 below).

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x x x ... x

x x x ... x x

and use the vectors (-1, 2) and (ceil(n/2), 1) as the Fokker block chromas. A Fokker block has the property that tempering out by each of the chromas gives two mosses. These correspond to the L = M and M = s temperings. [Proof to be continued...]

and use the vectors (-1, 2) and (ceil(n/2), 1) as the Fokker block chromas. A Fokker block has the property that tempering out by each of the chromas gives two mosses. These correspond to the L = M and M = s temperings. The L = s case follows by symmetry. [Proof to be continued...]

=== Proposition 2 (Odd GO scales are SGA) ===

@@ Line 34: / Line 34: @@
 # S = aX bY bZ is obtained from the (single-period) mos aX 2bW by replacing all the W's successively with alternating Y's and Z's (or alternating Z's and Y's for the other chirality).
 # The two alternants differ by replacing one Y with a Z.
-# ''S'' has the property that the following operations result in a mos: setting L = M, and setting M = s.
+# ''S'' has the property that the following operations result in a mos: setting L = M, setting L = s, and setting M = s.
 In particular, odd GO scales always satisfy these properties (see Proposition 2 below).
@@ Line 86: / Line 86: @@
   x x x ... x
   x x x ... x x
-and use the vectors (-1, 2) and (ceil(n/2), 1) as the Fokker block chromas. A Fokker block has the property that tempering out by each of the chromas gives two mosses. These correspond to the L = M and M = s temperings. [Proof to be continued...]
+and use the vectors (-1, 2) and (ceil(n/2), 1) as the Fokker block chromas. A Fokker block has the property that tempering out by each of the chromas gives two mosses. These correspond to the L = M and M = s temperings. The L = s case follows by symmetry. [Proof to be continued...]
 === Proposition 2 (Odd GO scales are SGA) ===