Generator-offset property: Difference between revisions

Inthar (talk | contribs)
Tags: Mobile edit Mobile web edit
Inthar (talk | contribs)
Tags: Mobile edit Mobile web edit
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These give exactly three distinct sizes for every interval class. Hence ''S'' is SV3.
These give exactly three distinct sizes for every interval class. Hence ''S'' is SV3.


In this case S has two chains of Q, one with floor(''n''/2) notes and and one with ceil(''n''/2) notes. Every instance of Q must be a ''k''-step, since by '''Z'''-linear independence Q = αa + βb + γc is the only way to write Q in the basis (a, b, c); so ''S'' is well-formed with respect to Q. Thus ''S'' also satisfies the generator-offset property with generator Q.
In this case S has two chains of Q, one with floor(''n''/2) notes and one offset by Q<sup>(''f''&minus;1)</sup>R with ceil(''n''/2) notes. Every instance of Q must be a ''k''-step, since by '''Z'''-linear independence Q = αa + βb + γc is the only way to write Q in the basis (a, b, c); so ''S'' is well-formed with respect to Q. Thus ''S'' also satisfies the generator-offset property with generator Q.


'''Case 2:''' μ ≥ ceil(''n''/2), i.e. Λ<sub>2</sub> has fewer β than β′.
'''Case 2:''' μ ≥ ceil(''n''/2), i.e. Λ<sub>2</sub> has fewer β than β′.