English

Letter graphs and geometric grid classes of permutations

Combinatorics 2022-06-03 v2

Abstract

We uncover a connection between two seemingly unrelated notions: lettericity, from structural graph theory, and geometric griddability, from the world of permutation patterns. Both of these notions capture important structural properties of their respective classes of objects. We prove that these notions are equivalent in the sense that a permutation class is geometrically griddable if and only if the corresponding class of inversion graphs has bounded lettericity.

Keywords

Cite

@article{arxiv.2107.03447,
  title  = {Letter graphs and geometric grid classes of permutations},
  author = {Bogdan Alecu and Robert Ferguson and Mamadou Moustapha Kanté and Vadim Lozin and Vincent Vatter and Viktor Zamaraev},
  journal= {arXiv preprint arXiv:2107.03447},
  year   = {2022}
}
R2 v1 2026-06-24T03:58:44.914Z