Quadratic Gröbner bases arising from partially ordered sets


  • Takayuki Hibi
  • Kazunori Matsuda
  • Akiyoshi Tsuchiya




The order polytope $\mathcal {O}(P)$ and the chain polytope $\mathcal {C}(P)$ associated to a partially ordered set $P$ are studied. In this paper, we introduce the convex polytope $\Gamma (\mathcal {O}(P), -\mathcal {C}(Q))$ which is the convex hull of $\mathcal {O}(P) \cup (-\mathcal {C}(Q))$, where both $P$ and $Q$ are partially ordered sets with $|P|=|Q|=d$. It will be shown that $\Gamma (\mathcal {O}(P), -\mathcal {C}(Q))$ is a normal and Gorenstein Fano polytope by using the theory of reverse lexicographic squarefree initial ideals of toric ideals.


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How to Cite

Hibi, T., Matsuda, K., & Tsuchiya, A. (2017). Quadratic Gröbner bases arising from partially ordered sets. MATHEMATICA SCANDINAVICA, 121(1), 19–25. https://doi.org/10.7146/math.scand.a-26246