Bonferroni-Galambos Inequalities for Partition Lattices

In this paper, we establish a new analogue of the classical Bonferroni inequalities and their improvements by Galambos for sums of type ∑ π∈P(U)(−1)(|π| − 1)!f(π) where U is a finite set, P(U) is the partition lattice of U and f : P(U) → R is some suitable non-negative function. Applications of this new analogue are given to counting connected k-uniform hypergraphs, network reliability, and cumulants.