English

Beyond the Runs Theorem

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

Abstract

Recently, a short and elegant proof was presented showing that a binary word of length nn contains at most n3n-3 runs. Here we show, using the same technique and a computer search, that the number of runs in a binary word of length nn is at most 2223n<0.957n\frac{22}{23}n<0.957n.

Cite

@article{arxiv.1502.04644,
  title  = {Beyond the Runs Theorem},
  author = {Johannes Fischer and Štěpán Holub and Tomohiro I and Moshe Lewenstein},
  journal= {arXiv preprint arXiv:1502.04644},
  year   = {2019}
}

Comments

New version with substantially improved bound and coauthors who carried out a similar research independently

R2 v1 2026-06-22T08:30:45.667Z