Generator-offset property: Difference between revisions
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# The two alternants differ by replacing one Y with a Z. | # 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'' 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). | In particular, odd GO scales always satisfy these properties (see Proposition 2 below). | ||
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The generator of aX 2bW must have an odd number of W steps; if it had an even number of W steps, it would be generated by stacking the generator of the mos aX bW' with W' = 2W, a contradiction. This with (4) immediately gives (5). | The generator of aX 2bW must have an odd number of W steps; if it had an even number of W steps, it would be generated by stacking the generator of the mos aX bW' with W' = 2W, a contradiction. This with (4) immediately gives (5). | ||
For (6 | For (6), odd-numbered SGA scales are [[Fokker block]]s* (in the 2-dimensional lattice generated by the generator and the offset). To see this, consider the following lattice depiction of such a scale: | ||
x x x ... x | x x x ... x | ||
x x x ... x x | x x x ... x x | ||