Interleaving: Difference between revisions
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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. | 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'' | Case 2: 1 < ''k'' < ''a'' + ''b''. | ||
Case 3: ''k'' = ''a'' + ''b''. | |||
== Generalizations == | == Generalizations == | ||