The three-state toric homogeneous Markov chain model has Markov degree two

Patrik Norén (1)

1 IST Austria - Institute of Science and Technology [Klosterneuburg, Austria]

We prove that the three-state toric homogenous Markov chain model has Markov degree two. In algebraic terminology this means, that a certain class of toric ideals are generated by quadratic binomials. This was conjectured by Haws, Martin del Campo, Takemura and Yoshida, who proved that they are generated by degree six binomials. 

Domaines: Géométrie algébrique [math.AG]

Patrik Norén. The three-state toric homogeneous Markov chain model has Markov degree two. MEGA'2013 (Special Issue), Jun 2013, Frankfurt am Main, Allemagne. ⟨hal-01022879⟩