English

Finding binary words with a given number of subsequences

Combinatorics 2022-10-04 v1

Abstract

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(lognloglogn)O(\log n \log \log n) with exactly nn subsequences; this can be improved to O(logn)O(\log n) under assumption of Zaremba's conjecture.

Keywords

Cite

@article{arxiv.2210.00342,
  title  = {Finding binary words with a given number of subsequences},
  author = {Radosław Żak},
  journal= {arXiv preprint arXiv:2210.00342},
  year   = {2022}
}
R2 v1 2026-06-28T02:31:51.770Z