论文信息 - On circle containment orders

On circle containment orders

A partially ordered set is called acircle containment order provided one can assign to each element of the poset a circle in the plane so thatx≤y iff the circle assigned tox is contained in the circle assigned toy. It has been conjectured that every finite three-dimensional partially ordered set is a circle containment order. We show that the infinite three dimensional posetZ3 isnot a circle containment order.

Edward R. Scheinerman | John C. Wierman | E. Scheinerman | J. Wierman

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