On the maximum size of an anti-chain of k-sets and convex pseudo-discs 1
Rom Pinchasi, Günter Rote · 2007
We answer a problem of Walter Morris about the maximum cardinality of an anti-chain composed of intersections of a given set of n points in the plane with half-planes. We approach this problem by establishing the equivalence with the problem of the maximum monotone path in an arrangement of n lines. A related problem on convex pseudo-discs is also discussed in the paper. 1