Interleaving: Difference between revisions
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=> '''δ''' - '''V''' = ‖''w''‖ = ‖''s''‖ - '''δ''' - '''W''' | => '''δ''' - '''V''' = ‖''w''‖ = ‖''s''‖ - '''δ''' - '''W''' | ||
=> 2'''δ''' + '''W''' = ‖''s''‖ + '''V'''. If this linear relation is trivial, the third letter '''U''' occurs an even number of times in ''s'', '''V''' occurs an odd number of times in ''s'', and '''W''' occurs an even number of times. Since gcd(''a'', ''b'') = 1, {'''U''', '''W'''} != {'''X''', '''Y'''}. | => 2'''δ''' + '''W''' = ‖''s''‖ + '''V'''. If this linear relation is nontrivial, it's a contradiction. If this linear relation is trivial, the third letter '''U''' occurs an even number of times in ''s'', '''V''' occurs an odd number of times in ''s'', and '''W''' occurs an even number of times. Since gcd(''a'', ''b'') = 1, {'''U''', '''W'''} != {'''X''', '''Y'''}. | ||
== Generalizations == | == Generalizations == | ||