Dohmen, Klaus; Tittmann, Peter Bonferroni-Galambos inequalities for partition lattices. (English) Zbl 1062.05015 Electron. J. Comb. 11, No. 1, Research paper R85, 9 p. (2004). Summary: We establish a new analogue of the classical Bonferroni inequalities and their improvements by Galambos for sums of type \(\sum_{\pi\in {\mathbb P}(U)} (-1)^{|\pi|-1} (|\pi|-1)! f(\pi)\) where \(U\) is a finite set, \({\mathbb P}(U)\) is the partition lattice of \(U\) and \(f:{\mathbb P}(U)\rightarrow{\mathbb R}\) is some suitable non-negative function. Applications of this new analogue are given to counting connected \(k\)-uniform hypergraphs, network reliability, and cumulants. Cited in 1 Document MSC: 05A18 Partitions of sets 60C05 Combinatorial probability 60E15 Inequalities; stochastic orderings 05C65 Hypergraphs Keywords:partition lattice; hypergraphs; network reliability; cumulants; inclusion-exclusion principle PDFBibTeX XMLCite \textit{K. Dohmen} and \textit{P. Tittmann}, Electron. J. Comb. 11, No. 1, Research paper R85, 9 p. (2004; Zbl 1062.05015) Full Text: EuDML EMIS