Markov chains of $Z$-oriented triangulations of surfaces
Combinatorics
2026-01-27 v1
Abstract
We consider triangulations of closed -dimensional (not necessarily orientable) surfaces. Any minimal set of zigzags that double covers the set of edges provides a -orientation of the triangulation. We introduce Markov chains of -oriented triangulations. Our main result is a characterization of their ergodicity. This topic is closely connected to coloring of Eulerian triangulations.
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}
}