Pfaffian Systems of A-Hypergeometric Equations I: Bases of Twisted Cohomology Groups
نویسندگان
چکیده
We consider bases of Pfaffian systems for A-hypergeometric systems. These are given by Gröbner deformations, they also provide bases for twisted cohomology groups. For a hypergeometric system associated with a class of order polytopes, these bases have a combinatorial description. The size of the bases associated with a subclass of the order polytopes has a growth rate of polynomial order.
منابع مشابه
Twisted cohomology and homology groups associated to the Riemann-Wirtinger integral
The Riemann-Wirtinger integral is a function defined by a definite integral on a complex torus whose integrand is a power product of the exponential function and theta functions. It was found as a special solution of the system of differential equations which governs the monodromy-preserving deformation of Fuchsian differential equations on the complex torus [11], [12]. The main purpose of this...
متن کاملTwisted period relations associated with con uent hypergeometric functions
1 Introduction Formulas of intersection numbers were given in [1] and [4] for twisted de-Rham cohomology groups and twisted homology groups dened by the connection r ! = d + ! associated with a 1-form ! with simple poles on the projective line P. In this paper, we present a denition of intersection pair-ing and a formula of intersection numbers between twisted homology groups associated with a ...
متن کاملThe Q-twisted Cohomology and the Q-hypergeometric Function at |q| = 1
We construct the q-twisted cohomology associated with the q-multiplicative function of Jordan-Pochhammer type at |q| = 1. In this framework, we prove the Heine’s relations and a connection formula for the q-hypergeometric function of the Barnes type. We also prove an orthogonality relation of the q-little Jacobi polynomials at |q| = 1.
متن کاملPfaffian Systems of A-Hypergeometric Systems II - Holonomic Gradient Method
We give two efficient methods to derive Pfaffian systems for A-hypergeometric systems for the application to the holonomic gradient method for statistics. We utilize the Hilbert driven Buchberger algorithm and Macaulay type matrices in the two methods.
متن کاملDigital cohomology groups of certain minimal surfaces
In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012