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We consider the problem of bounding the complexity of the k-th level in an arrangementof n curves or surfaces, a problem dual to, and an extension of, the well-knownk-set problem. Among other results, we prove a new bound, O(nk), on the complexityof the k-th level in an arrangement of n planes in R, or on the number of k-sets in a setof n points in three dimensions, and we show that the complexity of the k-th level in anarrangement of n line segments in the plane is O(n...

On Levels in Arrangements of Lines, Segments, Planes, and Triangles%