Note on hypergraphs and sphere orders

We show that each partial order ≤ of height 2 can be represented by spheres in Euclidean space, where inclusion represents ≤. If each element has at most k elements under it, we can do this in 2k ? 1-dimensional space. This extends a result (and a method) of Scheinerman for the case k = 2. © 1993 John Wiley & Sons, Inc.