MOS substitution: Difference between revisions

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=== If the template is a primitive MOS, and for some perfect generators <math>p_T, p_F, \ \left|p_T\right|_\mathbf{X} = \left|p_F\right|,</math> then MOS substitution yields almost parallelograms in the lattice ===

With the additional assumption that the number of '''X''' letters in a perfect generator ''p''''T'' of the template MOS be a generator class of the filling MOS, the generator sequence yields ''q'' parallel chains ''C''1,

..., ''C''''q'' of the aggregate generator. The offset between ''C''''i'' and ''C''''i''+1 is equal to subst(''p''''T'', '''X''', ''p''''F''), where ''p''''T'' and ''p''''F'' are perfect generators (of appropriate lengths) of the template and filling MOSes, respectively. The aggregate generator is subst((''p''''T'')''q'', '''X''', ''G''''r''), where ''G'' is the period of the filling MOS.

..., ''C''''q'' of the aggregate generator, the sum of the generators in the GS. The offset between ''C''''i'' and ''C''''i''+1 is equal to subst(''p''''T'', '''X''', ''p''''F''), where ''p''''T'' and ''p''''F'' are perfect generators (of appropriate lengths) of the template and filling MOSes, respectively. The aggregate generator is subst((''p''''T'')''q'', '''X''', ''G''''r''), where ''G'' is the period of the filling MOS.

Hence in the GS,

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 === If the template is a primitive MOS, and for some perfect generators <math>p_T, p_F, \ \left|p_T\right|_\mathbf{X} = \left|p_F\right|,</math> then MOS substitution yields almost parallelograms in the lattice ===
 With the additional assumption that the number of '''X''' letters in a perfect generator ''p''<sub>''T''</sub> of the template MOS be a generator class of the filling MOS, the generator sequence yields ''q'' parallel chains ''C''<sub>1</sub>,
-..., ''C''<sub>''q''</sub> of the aggregate generator. The offset between ''C''<sub>''i''</sub> and ''C''<sub>''i''+1</sub> is equal to subst(''p''<sub>''T''</sub>, '''X''', ''p''<sub>''F''</sub>), where ''p''<sub>''T''</sub> and ''p''<sub>''F''</sub> are perfect generators (of appropriate lengths) of the template and filling MOSes, respectively. The aggregate generator is  subst((''p''<sub>''T''</sub>)<sup>''q''</sup>, '''X''', ''G''<sup>''r''</sup>), where ''G'' is the period of the filling MOS.
+..., ''C''<sub>''q''</sub> of the aggregate generator, the sum of the generators in the GS. The offset between ''C''<sub>''i''</sub> and ''C''<sub>''i''+1</sub> is equal to subst(''p''<sub>''T''</sub>, '''X''', ''p''<sub>''F''</sub>), where ''p''<sub>''T''</sub> and ''p''<sub>''F''</sub> are perfect generators (of appropriate lengths) of the template and filling MOSes, respectively. The aggregate generator is  subst((''p''<sub>''T''</sub>)<sup>''q''</sup>, '''X''', ''G''<sup>''r''</sup>), where ''G'' is the period of the filling MOS.
 Hence in the GS,