Hypergeometric Polynomials and Integer Programming
Mutsumi Saito, Bernd Sturmfels, Nobuki Takayama · Compositio Mathematica · 1999
We examine connections between A-hypergeometric differential equations and the theory of integer programming. In the first part, we develop a ’hypergeometric sensitivity analysis‘ for small variations of constraint constants with creation operators and b-functions. In the second part, we study the indicial polynomial (b-function) along the hyperplane xi=0 via a correspondence between the optimal value of an integer programming problem and the roots of the indicial polynomial. Gröbner bases are used to prove theorems and give counter examples.