Generator-offset property: Difference between revisions
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=== Proposition 3 (Properties of even GO scales) === | === Proposition 3 (Properties of even GO scales) === | ||
A GO scale of even size where the generator g is an even-step (i.e. g subtends an even number of steps) has the following properties: | A primitive GO scale of even size where the generator g is an even-step (i.e. g subtends an even number of steps) has the following properties: | ||
# It is a union of two mosses of size ''n''/2 generated by g | # It is a union of two primitive mosses of size ''n''/2 generated by g | ||
# It is ''not'' SV3 | # It is ''not'' SV3 | ||
# It is ''not'' chiral | # It is ''not'' chiral | ||
# It is a mos word of two of the letters interleaved with the third letter, for example: XYXZXYXZXY. | # It is a primitive mos word of two of the letters interleaved with the third letter, for example: XYXZXYXZXY. | ||
==== Proof ==== | ==== Proof ==== | ||
(1) and (2) were proved in the proof of Proposition 1 (the part that we appeal to, from "all multiples of the generator g must be even-steps ..." to "These are all distinct by Z-linear independence", does not rely on ''S'' having the SGA property). (3) and (4) are easy to check using (1). | (1) and (2) were proved in the proof of Proposition 1 (the part that we appeal to, from "all multiples of the generator g must be even-steps ..." to "These are all distinct by Z-linear independence", does not rely on ''S'' having the SGA property). (3) and (4) are easy to check using (1). | ||