Generator-offset property: Difference between revisions
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=== Proposition 3 (Properties of even GO scales) === | === Proposition 3 (Properties of even GO scales) === | ||
GO | A GO scale of even size have the following properties: | ||
# | # It is a union of two mosses of size ''n''/2 generated by g | ||
# | # It is ''not'' SV3 | ||
# | # It is ''not'' chiral | ||
==== Proof ==== | ==== Proof ==== | ||
(1) and (2) were proved in the proof of Prop 1. (3) is easy to check using (1). | (1) and (2) were proved in the proof of Prop 1. (3) is easy to check using (1). | ||
Note that x<sup>''r''</sup>yx<sup>''r''</sup>z (generator x, offset x<sup>''r''</sup>y) is a counterexample to the claim that the offset must be an odd number of steps. | |||
=== Theorem 4 (Classification of PWF scales) === | === Theorem 4 (Classification of PWF scales) === | ||