Interleaving: Difference between revisions

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Moreover, the offset '''δ''' = '''Z''', i.e. ''S''2 is separated by the interval '''Z''' to the right of ''S''1.

If any maximal subword of consecutive '''Z'''s has ''q'' > 1, then the scale can be split into two subwords of ~~the same~~ length, ''w''1 with the maximal number of consecutive '''Z''''s and ''w''2 with the minimal number of '''Z'''s.

If any maximal subword of consecutive '''Z'''s has ''q'' > 1, then the scale can be split into two subwords of length ''a'' + ''b'', ''w''1 with the maximal number of consecutive '''Z''''s and ''w''2 with the minimal number of '''Z'''s.

Scoot ''w''1 to the right one step at a time until it loses one '''Z''', or scoot ''w''2 to the right until it gains one '''Z'''. Because of the offset and because either ''w''1 or ''w''2 begins in ''S''1 (because ''a'' + ''b'' is odd), this proves that a non-'''Z''' letter is equal to '''Z'''. Hence ''q'' = 1, as desired.

@@ Line 44: / Line 44: @@
 Moreover, the offset '''δ''' = '''Z''', i.e. ''S''<sub>2</sub> is separated by the interval '''Z''' to the right of ''S''<sub>1</sub>.
-If any maximal subword of consecutive '''Z'''s has ''q'' > 1, then the scale can be split into two subwords of the same length, ''w''<sub>1</sub> with the maximal number of consecutive '''Z''''s and ''w''<sub>2</sub> with the minimal number of '''Z'''s.
+If any maximal subword of consecutive '''Z'''s has ''q'' > 1, then the scale can be split into two subwords of length ''a'' + ''b'', ''w''<sub>1</sub> with the maximal number of consecutive '''Z''''s and ''w''<sub>2</sub> with the minimal number of '''Z'''s.
 Scoot ''w''<sub>1</sub> to the right one step at a time until it loses one '''Z''', or scoot ''w''<sub>2</sub> to the right until it gains one '''Z'''. Because of the offset and because either ''w''<sub>1</sub> or ''w''<sub>2</sub> begins in ''S''<sub>1</sub> (because ''a'' + ''b'' is odd), this proves that a non-'''Z''' letter is equal to '''Z'''. Hence ''q'' = 1, as desired.