Recursive structure of MOS scales: Difference between revisions
m →Special cases: Removed bold in header |
m →Uniqueness and existence of the generator: the generator is L, not s |
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Every MOS can be reduced to nL 1s (or 1L ns). Each step of the reduction decreases either the number of L's or the number of s's (or both), so one of them must reach 1 at some point. ''(note that reducing further gets us to 1L 0s, which has a period, but no generator per se)'' | Every MOS can be reduced to nL 1s (or 1L ns). Each step of the reduction decreases either the number of L's or the number of s's (or both), so one of them must reach 1 at some point. ''(note that reducing further gets us to 1L 0s, which has a period, but no generator per se)'' | ||
It is clear that the MOS nL 1s has a unique generator, | It is clear that the MOS nL 1s has a unique generator, L (or its inversion). However, the previous proof showed that reduction reflects generators, and so by induction all MOS scales have a single generator. | ||
=== Child MOSes exist === | === Child MOSes exist === | ||