article published yes Patrik Noren author 46870C74-F248-11E8-B48F-1D18A9856A87 CaUh department We prove that the three-state toric homogeneous Markov chain model has Markov degree two. In algebraic terminology this means, that a certain class of toric ideals is 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. Elsevier2015 eng 1207.0077 00034776760001610.1016/j.jsc.2014.09.014 68/Part 2May-June285 - 296 Noren, Patrik. “The Three-State Toric Homogeneous Markov Chain Model Has Markov Degree Two.” <i>Journal of Symbolic Computation</i>, vol. 68/Part 2, no. May-June, Elsevier, 2015, pp. 285–96, doi:<a href="https://doi.org/10.1016/j.jsc.2014.09.014">10.1016/j.jsc.2014.09.014</a>. Noren, P. (2015). The three-state toric homogeneous Markov chain model has Markov degree two. <i>Journal of Symbolic Computation</i>. Elsevier. <a href="https://doi.org/10.1016/j.jsc.2014.09.014">https://doi.org/10.1016/j.jsc.2014.09.014</a> Noren P. 2015. The three-state toric homogeneous Markov chain model has Markov degree two. Journal of Symbolic Computation. 68/Part 2(May-June), 285–296. P. Noren, “The three-state toric homogeneous Markov chain model has Markov degree two,” <i>Journal of Symbolic Computation</i>, vol. 68/Part 2, no. May-June. Elsevier, pp. 285–296, 2015. Noren, Patrik. “The Three-State Toric Homogeneous Markov Chain Model Has Markov Degree Two.” <i>Journal of Symbolic Computation</i>. Elsevier, 2015. <a href="https://doi.org/10.1016/j.jsc.2014.09.014">https://doi.org/10.1016/j.jsc.2014.09.014</a>. P. Noren, Journal of Symbolic Computation 68/Part 2 (2015) 285–296. Noren P. The three-state toric homogeneous Markov chain model has Markov degree two. <i>Journal of Symbolic Computation</i>. 2015;68/Part 2(May-June):285-296. doi:<a href="https://doi.org/10.1016/j.jsc.2014.09.014">10.1016/j.jsc.2014.09.014</a> 19972018-12-11T11:55:07Z2025-09-23T14:17:34Z