Markov chains of $Z$-oriented triangulations of surfaces
Abstract
We consider triangulations of closed $2$-dimensional (not necessarily orientable) surfaces. Any minimal set of zigzags that double covers the set of edges provides a $z$-orientation of the triangulation. We introduce Markov chains of $z$-oriented triangulations. Our main result is a characterization of their ergodicity. This topic is closely connected to coloring of Eulerian triangulations.
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Combinatorial Mathematics
Advanced Graph Theory Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 25 January 2026
- Document type
- Preprint