Generator-offset property: Difference between revisions
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# If ''n'' is odd, ''S'' = ''a''X ''b''Y ''b''Z is obtained from some mode of the (single-period) mos ''a''X 2''b''W 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, fixing the mode of ''a''X 2''b''W). The two alternants differ by replacing one Y with a Z. | # If ''n'' is odd, ''S'' = ''a''X ''b''Y ''b''Z is obtained from some mode of the (single-period) mos ''a''X 2''b''W 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, fixing the mode of ''a''X 2''b''W). The two alternants differ by replacing one Y with a Z. | ||
# If ''n'' is odd, ''S'' is pairwise-mos. That is, the following operations each result in a [[mos]]: setting L = M, setting L = s, and setting M = s. | # If ''n'' is odd, ''S'' is pairwise-mos. That is, the following operations each result in a [[mos]]: setting L = M, setting L = s, and setting M = s. | ||
# If ''n'' is odd, ''S'' is elimination-mos. That is, ''E''<sub>X</sub>, ''E''<sub>Y</sub>, ''E''<sub>Z</sub> are all mosses. | # If ''n'' is odd, ''S'' is elimination-mos. That is, ''E''<sub>X</sub>(''S''), ''E''<sub>Y</sub>(''S''), ''E''<sub>Z</sub>(''S'') are all mosses. | ||
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). | ||