2011/08/02 by David Haws, Abraham Martin Del Campo, Haws, David +4
Mathematics · #05cxx #52B20 #60J10 #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #Markov Chains and Monte Carlo Methods #Statistics Theory (math.ST) #math.CO #math.ST #msc:05cxx #msc:52B20 #msc:60J10 #stat.TH
paper · pdf · doi:10.48550/arxiv.1108.0481
openalex publication_date 2011/08/02 · arxiv created 2011/08/03 · arxiv updated 2011/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.