论文标题
极端无重叠和极端$β$ - 无二进制单词
Extremal overlap-free and extremal $β$-free binary words
论文作者
论文摘要
如果每个单词从$ w $获得的每个单词通过从任何位置插入单个字母，则无重叠（或$β$ - free）单词$ w $在固定的字母$σ$上都是极端的。我们发现所有允许极端无重叠二进制单词的长度。对于每个扩展的实际数量$β$，使$ 2^+\leqβ\ leq 8/3 $，我们表明有任意长的极端$β$ - 无二进制单词。
An overlap-free (or $β$-free) word $w$ over a fixed alphabet $Σ$ is extremal if every word obtained from $w$ by inserting a single letter from $Σ$ at any position contains an overlap (or a factor of exponent at least $β$, respectively). We find all lengths which admit an extremal overlap-free binary word. For every extended real number $β$ such that $2^+\leqβ\leq 8/3$, we show that there are arbitrarily long extremal $β$-free binary words.
