The three-state toric homogeneous Markov chain model has Markov degree   two
  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 binomials of degree six or less. 
Patrik Nor\'en
math.ST math.AC math.CO stat.TH