English

More ties than we thought

Formal Languages and Automata Theory 2015-05-07 v2 Computational Geometry Combinatorics General Topology

Abstract

We extend the existing enumeration of neck tie-knots to include tie-knots with a textured front, tied with the narrow end of a tie. These tie-knots have gained popularity in recent years, based on reconstructions of a costume detail from The Matrix Reloaded, and are explicitly ruled out in the enumeration by Fink and Mao (2000). We show that the relaxed tie-knot description language that comprehensively describes these extended tie-knot classes is context free. It has a regular sub-language that covers all the knots that originally inspired the work. From the full language, we enumerate 266 682 distinct tie-knots that seem tie-able with a normal neck-tie. Out of these 266 682, we also enumerate 24 882 tie-knots that belong to the regular sub-language.

Cite

@article{arxiv.1401.8242,
  title  = {More ties than we thought},
  author = {Dan Hirsch and Ingemar Markström and Meredith L Patterson and Anders Sandberg and Mikael Vejdemo-Johansson},
  journal= {arXiv preprint arXiv:1401.8242},
  year   = {2015}
}

Comments

Accepted at PeerJ Computer Science 12 pages, 6 color photographs

R2 v1 2026-06-22T02:58:46.043Z