%0 Journal Article
%T Computing the partition function for perfect matchings in a hypergraph
%A Alexander Barvinok
%A Alex Samorodnitsky
%J Mathematics
%D 2010
%I arXiv
%X Given non-negative weights w_S on the k-subsets S of a km-element set V, we consider the sum of the products w_{S_1} ... w_{S_m} for all partitions V = S_1 cup ... cup S_m into pairwise disjoint k-subsets S_i. When the weights w_S are positive and within a constant factor, fixed in advance, of each other, we present a simple polynomial time algorithm to approximate the sum within a polynomial in m factor. In the process, we obtain higher-dimensional versions of the van der Waerden and Bregman-Minc bounds for permanents. We also discuss applications to counting of perfect and nearly perfect matchings in hypergraphs.
%U http://arxiv.org/abs/1009.2397v3