3 problems

Markov group containment conjecture. For every $n\geq 1$, the associated Markov group is contained in the corresponding Galois group:

A Markov chain defined solely at the level of substitution matrices may be multiplicatively closed without being given in terms of rate matrices. Lie-algebra necessity conjecture.…

Fix integers $T\geq 3$ and $S\geq 3$. Consider the toric ideals of the homogeneous Markov chain model on $S$ states. Homogeneous Markov chain degree-bound conjecture. These toric i…