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arXiv · 2601.17943

Markov chains of $Z$-oriented triangulations of surfaces

Adam Tyc
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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.

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Adam Tyc. 2026-01-25. Markov chains of $Z$-oriented triangulations of surfaces. https://arxiv.org/abs/2601.17943

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