Interleaving: Difference between revisions
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If ''k'' > 1, stack the word of ''k''-steps in the scale, yielding a circular word ''T''. Since ''k'' is odd, the letters of this word alternate between beginning in ''S''<sub>1</sub> and beginning in ''S''<sub>2</sub>. By a reasoning similar to the above, ''T'' has a letter '''δ''' between its two mutually interleaved strands. (To be continued) | If ''k'' > 1, stack the word of ''k''-steps in the scale, yielding a circular word ''T''. Since ''k'' is odd, the letters of this word alternate between beginning in ''S''<sub>1</sub> and beginning in ''S''<sub>2</sub>. By a reasoning similar to the above, ''T'' has a letter '''δ''' between its two mutually interleaved strands. (To be continued) | ||
Suppose that '''δ''' = ''m'''''X''' + ''n'''''Y''' + ''p'''''Z''', ''m'' + ''n'' + ''p'' = ''k''. | |||
Case 3: gcd(2(''a'' + ''b''), ''k'') > 1. ''k'' being even contradicts the interleaving property, hence ''k'' = ''a'' + ''b''. (To be continued) | Case 3: gcd(2(''a'' + ''b''), ''k'') > 1. ''k'' being even contradicts the interleaving property, hence ''k'' = ''a'' + ''b''. (To be continued) | ||