Pfaffian Systems of A-Hypergeometric Equations I: Bases of Twisted   Cohomology Groups
  This is the third revision. We study bases of Pfaffian systems for $A$-hypergeometric system. Gr\"obner deformations give bases. These bases also give those for twisted cohomology groups. For hypergeometric system associated to a class of order polytopes, these bases have a combinatorial description. The size of the bases associated to a subclass of the order polytopes have the growth rate of the polynomial order. Bases associated to two chain posets and bouquets are studied. 
Takayuki Hibi, Kenta Nishiyama, Nobuki Takayama
math.CA cs.SC math.CO