Pfaffian Equations and Contiguity Relations of the Hypergeometric Function of Type (k+1, k+n+2) and Their Applications

Abstract

We study the structures of Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1, k+n+2) by using twisted cohomology groups and the intersection forms on them. We apply our results to algebraic statistics; we give an algorithm for numerical evaluation of the normalizing constants of two way contingency tables with fixed marginal sums.