论文标题
组合四面体连锁和相关的马尔可夫链中的曲折
Zigzags in combinatorial tetrahedral chains and the associated Markov chain
论文作者
论文摘要
嵌入在表面中的图形中的曲折是边缘的循环序列，其任何两个连续的边缘都不同，具有共同的顶点并且属于同一面。我们研究了随机构建的组合四面体链中的曲折。每个这样的连锁店最多都包含$ 3 $锯齿形的曲折。主要的结果是一个随机构造的四面体链的概率的极限，完全含有$ k \ in \ {1,2,3 \} $ zigzags，以逆转其长度接近无穷大。我们的关键工具是马尔可夫链，其状态为$ z $ - 单体粒子类型。
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 $3$ zigzags up to reversing. The main result is the limit of the probability that a randomly constructed tetrahedral chain contains precisely $k\in\{1,2,3\}$ zigzags up to reversing as its length approaches infinity. Our key tool is the Markov chain whose states are types of $z$-monodromies.
