三态环面齐次马尔可夫链模型最小马尔可夫基的度界
Degree Bounds for a Minimal Markov Basis for the Three-State Toric Homogeneous Markov Chain Model
摘要：
本文研究了三状态复曲面齐次马尔可夫链模型及其三种特殊情况，即：（i）当初态参数为常数时，（ii）无自环时，（iii）当这两种情况同时满足时。作为一个关键的工具，与模型相关联的有向多重图，状态图，我们给出了一个界限上的顶点数的多面体与模型，它不依赖于时间。在此基础上，我们还猜想了多胞形的f-向量的稳定性，分析了半群的正规性，给出了马氏基的度的理论界。
英文摘要：
We study the three state toric homogeneous Markov chain model and three special cases of it, namely: (i) when the initial state parameters are constant, (ii) without self-loops, and (iii) when both cases are satisfied at the same time. Using as a key tool a directed multigraph associated to the model, the state-graph, we give a bound on the number of vertices of the polytope associated to the model which does not depend on the time. Based on our computations, we also conjecture the stabilization of the f-vector of the polytope, analyze the normality of the semigroup, give conjectural bounds on the degree of the Markov bases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
