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arXiv · 1506.00802

Quadratic Gr\"obner bases arising from partially ordered sets

Takayuki Hibi·Kazunori Matsuda·Akiyoshi Tsuchiya
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Abstract

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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Takayuki Hibi, Kazunori Matsuda, Akiyoshi Tsuchiya. 2015-06-02. Quadratic Gr\"obner bases arising from partially ordered sets. https://arxiv.org/abs/1506.00802

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