English

Prefix frequency of lost positions

Formal Languages and Automata Theory 2019-12-18 v2 Discrete Mathematics

Abstract

The concept of "lost positions" is a recently introduced tool for counting the number of runs in words. We investigate the frequency of lost positions in prefixes of words. This leads to an algorithm that allows to show, using an extensive computer search, that the asymptotic density of runs in binary words is less than 183/1930.9482183/193\approx 0.9482.

Keywords

Cite

@article{arxiv.1606.01274,
  title  = {Prefix frequency of lost positions},
  author = {Štěpán Holub},
  journal= {arXiv preprint arXiv:1606.01274},
  year   = {2019}
}

Comments

Expanded and corrected version with examples and figures

R2 v1 2026-06-22T14:17:25.878Z