2015/05/16 by Takayuki Hibi, Hibi, Takayuki, Kazunori Matsuda +1 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13P10 #Secondary 52B20
paper · pdf · doi:10.48550/arxiv.1505.04289
openalex publication_date 2015/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let P and Q be finite partially ordered sets on [d] = \1, …, d\, and O(P) ⊂ ℝd and O(Q) ⊂ ℝd their order polytopes. The twinned order polytope of P and Q is the convex polytope Δ(P,-Q) ⊂ ℝd which is the convex hull of O(P) ∪ (- O(Q)). It follows that the origin of ℝd belongs to the interior of Δ(P,-Q) if and only if P and Q possess a common linear extension. It will be proved that, when the origin of ℝd belongs to the interior of Δ(P,-Q), the toric ideal of Δ(P,-Q) possesses a quadratic Gröbner basis with respect to a reverse lexicographic order for which the variable corresponding to the origin is smallest. Thus in particular if P and Q possess a common linear extension, then the twinned order polytope Δ(P,-Q) is a normal Gorenstein Fano polytope.