Improved Bonferroni inequalities via union-closed set systems

[摘要] By applying a recent result of Naiman and Wynn on abstract tubes, we establish a new improvement of the classical Bonferroni inequalities for any finite collection of sets {A(nu)} (nu epsilon) nu associated with an additional structure, which is assumed to be given by a union-closed set X of non-empty subsets of V such that boolean AND(x epsilon)XA(x)subset of or equal to U(upsilon is not an element of X)A(nu) for any X epsilon X. The result generalizes several other results from the literature. (C) 2000 Academic Press.

[发布日期] 2000-10-01

[关键词] inclusion-exclusion;abstract tube;Euler characteristic