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 form on them. We apply our results to algebraic statistics; numerical evaluation of the normalizing constants of two way contingency tables with fixed marginal sums.