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

2012/12/25 by Takayuki Hibi, Hibi, Takayuki, Kenta Nishiyama +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.1212.6103

openalex publication_date 2012/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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

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