Pfaffian Systems of A-Hypergeometric Equations I: Bases of Twisted Cohomology Groups

Abstract

This is the third revision. We study bases of Pfaffian systems for $A$-hypergeometric system. Gröbner 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.

References in corpus (1)

• Holonomic Gradient Descent for the Fisher-Bingham Distribution on the $d$-dimensional Sphere

Cited by in corpus (1)

• Pfaffian Systems of A-Hypergeometric Systems II --- Holonomic Gradient Method