Interleaving: Difference between revisions
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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 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. | ||
Scoot ''w''<sub>1</sub> to the right one step at a time until it loses one '''Z'''. Because of the offset, this proves that a non-'''Z''' letter is equal to '''Z'''. Hence ''q'' = 1, as desired. | 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. | ||
Case 2: ''k'' ≥ 3. | Case 2: ''k'' ≥ 3. | ||