Inclusion-Exclusion-Bonferroni Identities and Inequalities for Discrete Tube-Like Problems via Euler Characteristics

Improved Inclusion-Exclusion Identities and Bonferroni Inequalities with Applications to Reliability Analysis of Coherent Systems

Improved inclusion-exclusion identities via closure operators

Improved inclusion-exclusion identities via closure operators Klaus Dohmen Department of Computer Science, Humboldt-University Berlin, Unter den Linden 6, D-10099 Berlin, Germany E-mail: [email protected] received March 24, 1999, revised September 6, 1999, accepted April 15, 2000. Let be a finite family of sets. We establish an improved inclusion-exclusion identity for each closure...

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...

Improved Inclusion-Exclusion Identities and Inequalities Based on a Particular Class of Abstract Tubes

Recently, Naiman and Wynn introduced the concept of an abstract tube in order to obtain improved inclusion-exclusion identities and inequalities that involve much fewer terms than their classical counterparts. In this paper, we introduce a particular class of abstract tubes which plays an important role with respect to chromatic polynomials and network reliability. The inclusionexclusion identi...

Inclusion-Exclusion Principles for Convex Hulls and the Euler Relation

Abstract. Consider n points X1, . . . ,Xn in R and denote their convex hull by Π. We prove a number of inclusion-exclusion identities for the system of convex hulls ΠI := conv(Xi : i ∈ I), where I ranges over all subsets of {1, . . . , n}. For instance, denoting by ck(X) the number of k-element subcollections of (X1, . . . ,Xn) whose convex hull contains a point X ∈ R, we prove that c1(X) − c2(...