Hypermultitrees and sharp Bonferroni inequalities

Bonferroni-type inequalities and binomially bounded functions

We present a unified approach to an important subclass of Bonferroni-type inequalities by considering so-called binomially bounded functions. Our main result associates with each binomially bounded function a Bonferroni-type inequality. By appropriately choosing this function, several well-known and new results are deduced.

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 cum...

Support Approximations Using Bonferroni-Type Inequalities

Improved Bonferroni Inequalities via Abstract Tubes - ReadingSample

1 Introduction and Overview Many problems in combinatorics, number theory, probability theory, reliability theory and statistics can be solved by applying a unifying method, which is known as the principle of inclusion-exclusion. The principle of inclusion-exclusion expresses the indicator function of a union of finitely many sets as an alternating sum of indicator functions of their intersecti...

Sharp Boundary Trace Inequalities

This paper describes sharp inequalities for the trace of Sobolev functions on the boundary of a bounded region Ω ⊂ R . The inequalities bound (semi-)norms of the boundary trace by certain norms of the function and its gradient on the region and two specific constants kρ and kΩ associated with the domain and a weight function. These inequalities are sharp in that there are functions for which eq...