Quadratic Gröbner bases arising from partially ordered sets

• Takayuki Hibi ^[1] ; Kazunori Matsuda ^[1] ; Akiyoshi Tsuchiya ^[1]
  1. [1] Osaka University

     Osaka University

     Kita Ku, Japón

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 121, Nº 1, 2017, págs. 19-25
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.