Resumen de Quadratic Gröbner bases arising from partially ordered sets

Takayuki Hibi, Kazunori Matsuda, Akiyoshi Tsuchiya

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