English

$Z$-knotted and $Z$-homogeneous triangulations of surfaces

Combinatorics 2020-08-20 v1

Abstract

A triangulation is called zz-knotted if it has a single zigzag (up to reversing). A zz-orientation on a triangulation is a minimal collection of zigzags which double covers the set of edges. An edge is of type I if zigzags from the zz-orientation pass through it in different directions, otherwise this edge is of type II. If all zigzags from the zz-orientation contain precisely two edges of type I after any edge of type II, then the zz-oriented triangulation is said to be zz-homogeneous. We describe an algorithm transferring each zz-homogeneous trianguation to other zz-homogeneous triangulation which is also zz-knotted.

Keywords

Cite

@article{arxiv.2008.08126,
  title  = {$Z$-knotted and $Z$-homogeneous triangulations of surfaces},
  author = {Adam Tyc},
  journal= {arXiv preprint arXiv:2008.08126},
  year   = {2020}
}