Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Degree Bounds for a Minimal Markov Basis for the Three-State Toric
  Homogeneous Markov Chain Model   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.

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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci