Generator-offset property: Difference between revisions

Inthar (talk | contribs)
Inthar (talk | contribs)
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# ''S'' is generated by two chains of stacked generators g separated by a fixed offset δ; either both chains are of size ''n''/2 (implying ''n'' is even), or one chain has size (''n'' + 1)/2 and the second has size (''n'' − 1)/2 (implying ''n'' is odd).  
# ''S'' is generated by two chains of stacked generators g separated by a fixed offset δ; either both chains are of size ''n''/2 (implying ''n'' is even), or one chain has size (''n'' + 1)/2 and the second has size (''n'' − 1)/2 (implying ''n'' is odd).  
# The scale is ''well-formed'' with respect to g, i.e. all occurrences of the generator g are ''k''-steps for a fixed ''k''.
# The scale is ''well-formed'' with respect to g, i.e. all occurrences of the generator g are ''k''-steps for a fixed ''k''.
This doesn't imply that g<sub>1</sub> and g<sub>2</sub> are the same number of scale steps. For example, 5-limit [[blackdye]] has g<sub>1</sub> = 9/5 (a 9-step)  and g<sub>2</sub> = 5/3 (a 7-step).


== Open conjectures ==
== Open conjectures ==