Abstract

The inclusion-exclusion formula expresses the size of the union of a family of sets in terms of the sizes of intersections of all subfamilies. N. Linial and N. Nisan use linear programming to approximate the size of the union when the intersection sizes are known only for certain subfamilies. In this article we use purely combinatorial methods to generalize some of their results. As an application we will construct a contrast optimal $\left(n-1\right)$-out-of-$n$ visual cryptography scheme.

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Mathematical Subject Classification 2000

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