Fraenkel word: Difference between revisions
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=== Fraenkel words are balanced === | === Fraenkel words are balanced === | ||
{{theorem|contents=For all ''n'' ≥ 1, the ''n''-ary Fraenkel word is [[balanced]] as a circular word.}} | {{theorem|contents=For all ''n'' ≥ 1, the ''n''-ary Fraenkel word is [[balanced]] as a circular word.}} | ||
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To prove this, we prove the following lemmas by induction on ''n'': | To prove this, we prove the following lemmas by induction on ''n'': | ||
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TODO: Handle the case where the subword ''w'' of ''F''<sub>''n''</sub> is a concatenation of a suffix of ''G''<sub>''n''</sub> and a prefix of ''G''<sub>''n''</sub>. | TODO: Handle the case where the subword ''w'' of ''F''<sub>''n''</sub> is a concatenation of a suffix of ''G''<sub>''n''</sub> and a prefix of ''G''<sub>''n''</sub>. | ||
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== Open problems == | == Open problems == | ||