English

Markov chains of $Z$-oriented triangulations of surfaces

Combinatorics 2026-01-27 v1

Abstract

We consider triangulations of closed 22-dimensional (not necessarily orientable) surfaces. Any minimal set of zigzags that double covers the set of edges provides a zz-orientation of the triangulation. We introduce Markov chains of zz-oriented triangulations. Our main result is a characterization of their ergodicity. This topic is closely connected to coloring of Eulerian triangulations.

Keywords

Cite

@article{arxiv.2601.17943,
  title  = {Markov chains of $Z$-oriented triangulations of surfaces},
  author = {Adam Tyc},
  journal= {arXiv preprint arXiv:2601.17943},
  year   = {2026}
}