MOS substitution: Difference between revisions

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== Facts ==

The following holds for <math>S = \mathsf{MOS\_subst}(a, b, c; \mathbf{L}, \mathbf{s}; k)</math> (and after ~~replacing~~ <math>\mathbf{L}</math> with <math>\mathbf{m}</math> and <math>a</math> with <math>b,</math> for <math>\mathsf{MOS\_subst}(a, b, c; \mathbf{m}, \mathbf{s}; k)</math> as well):

The following holds for <math>S = \mathsf{MOS\_subst}(a, b, c; \mathbf{L}, \mathbf{s}; k)</math> (and after switching <math>\mathbf{L}</math> with <math>\mathbf{m}</math> and <math>a</math> with <math>b,</math> for <math>\mathsf{MOS\_subst}(a, b, c; \mathbf{m}, \mathbf{s}; k)</math> as well):

Let <math>\mathsf{MOS}(a,b;k)(\mathbf{x}, \mathbf{y})</math> be the mode of <math>a\mathbf{x}b\mathbf{y}</math> that would have brightness <math>k</math> if <math>\mathbf{x}</math> were <math>\mathbf{L}</math> and <math>\mathbf{y}</math> were <math>\mathbf{s}.</math> For example, <math>\mathsf{MOS}(5,2;5)(\mathbf{x},\mathbf{y}) = \mathbf{xxyxxxy}.</math> Let <math> n = a+b+c</math> and <math>q = (a + c)/(a,c)</math>.

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 == Facts ==
-The following holds for <math>S = \mathsf{MOS\_subst}(a, b, c; \mathbf{L}, \mathbf{s}; k)</math> (and after replacing <math>\mathbf{L}</math> with <math>\mathbf{m}</math> and <math>a</math> with <math>b,</math> for <math>\mathsf{MOS\_subst}(a, b, c; \mathbf{m}, \mathbf{s}; k)</math> as well):
+The following holds for <math>S = \mathsf{MOS\_subst}(a, b, c; \mathbf{L}, \mathbf{s}; k)</math> (and after switching <math>\mathbf{L}</math> with <math>\mathbf{m}</math> and <math>a</math> with <math>b,</math> for <math>\mathsf{MOS\_subst}(a, b, c; \mathbf{m}, \mathbf{s}; k)</math> as well):
 Let <math>\mathsf{MOS}(a,b;k)(\mathbf{x}, \mathbf{y})</math> be the mode of <math>a\mathbf{x}b\mathbf{y}</math> that would have brightness <math>k</math> if <math>\mathbf{x}</math> were  <math>\mathbf{L}</math> and <math>\mathbf{y}</math> were  <math>\mathbf{s}.</math> For example, <math>\mathsf{MOS}(5,2;5)(\mathbf{x},\mathbf{y}) = \mathbf{xxyxxxy}.</math> Let <math> n = a+b+c</math> and <math>q = (a + c)/(a,c)</math>.