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Hypergeometric Polynomials and Integer Programming

Published online by Cambridge University Press:  04 December 2007

MUTSUMI SAITO ,
BERND STURMFELS  and
NOBUKI TAKAYAMA
MUTSUMI SAITO
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo, Japan.
BERND STURMFELS
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA and Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan
NOBUKI TAKAYAMA
Affiliation:
Department of Mathematics, Kobe University, Kobe, Japan.
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Abstract

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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.

Keywords

A-hypergeometric functionGKZ-systeminteger programmingb-functionindical polynomialGröbner basis.
Type
Research Article
Information
Compositio Mathematica , Volume 115 , Issue 2 , February 1999 , pp. 231 - 240
Copyright
© 1999 Kluwer Academic Publishers