Generator-offset property: Difference between revisions

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# 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, setting L = s, and setting M = s.

# ''S'' is a billiard scale. In particular, ''S'' is elimination-mos: setting any one step size of ''S'' equal to 0 yields a mos.

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

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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. The L = s case follows by symmetry.

For (7), Fokker blocks are [[billiard scale]]s by the first definition of the Fokker block. Hence ''S'' is elimination-mos, which implies that setting any one step size equal to 0 yields a mos.

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

@@ Line 35: / Line 35: @@
 # 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, setting L = s, and setting M = s.
+# ''S'' is a billiard scale. In particular, ''S'' is elimination-mos: setting any one step size of ''S'' equal to 0 yields a mos.
 In particular, odd GO scales always satisfy these properties (see Proposition 2 below).
@@ Line 87: / Line 89: @@
   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. The L = s case follows by symmetry.
+For (7), Fokker blocks are [[billiard scale]]s by the first definition of the Fokker block. Hence ''S'' is elimination-mos, which implies that setting any one step size equal to 0 yields a mos.
 === Proposition 2 (Odd GO scales are SGA) ===