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| | The Mathematics of Words (Site not responding. Last check: 2007-11-06) |
 | | This is defined as a word which does not contain any repeated sequences after allowing for permutations: for example, bacadcabda can be rearranged to form bacadbacad by rearranging its last five letters. |
 | | For alphabets of size two, cadences of length 3, 4 and 5 must appear in all words of lengths 9, 35, and 178, respectively, and for alphabets of size three, cadences of length 3 must appear in all words of length 27. |
 | | Rephrasing the first result, the longest words containing only two different letters and no cadences of length 3 are only 8 letters long; the only examples of such words are aabbaabb, abbaabba and ababbaba. |
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