论文标题
找到具有给定数量子序列的二进制单词
Finding binary words with a given number of subsequences
论文作者
论文摘要
我们将二进制单词与给定数量的子序列与给定的分母的持续分数相关联。我们推断出有长度为$ o（\ log n \ log \ log n）$的二进制字符串，恰好是$ n $子序列；在Zaremba的猜想假设下，这可以将其提高到$ O（\ log n）$。
We relate binary words with a given number of subsequences to continued fractions of rational numbers with a given denominator. We deduce that there are binary strings of length $O(\log n \log \log n)$ with exactly $n$ subsequences; this can be improved to $O(\log n)$ under assumption of Zaremba's conjecture.
