On the maximum size of an anti-chain of linearly separable sets and convex pseudo-discs
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چکیده
We answer a question raised by Walter Morris, and independently by Alon Efrat, 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.
منابع مشابه
On the maximum size of an anti-chain of k-sets and convex pseudo-discs
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.
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تاریخ انتشار 2008