Zigzags in combinatorial tetrahedral chains and the associated Markov chain
Combinatorics
2022-06-22 v1
Abstract
Zigzags in graphs embedded in surfaces are cyclic sequences of edges whose any two consecutive edges are different, have a common vertex and belong to the same face. We investigate zigzags in randomly constructed combinatorial tetrahedral chains. Every such chain contains at most zigzags up to reversing. The main result is the limit of the probability that a randomly constructed tetrahedral chain contains precisely zigzags up to reversing as its length approaches infinity. Our key tool is the Markov chain whose states are types of -monodromies.
Keywords
Cite
@article{arxiv.2206.09830,
title = {Zigzags in combinatorial tetrahedral chains and the associated Markov chain},
author = {Adam Tyc},
journal= {arXiv preprint arXiv:2206.09830},
year = {2022}
}