Abstract
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 posetZ 3 isnot a circle containment order.
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Communicated by I. Rival
Research supported in part by the Office of Naval Research, contract number N00014-85-K0622.
Research supported in part by National Science Foundation, grant number DMS-8403646.
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Scheinerman, E.R., Wierman, J.C. On circle containment orders. Order 4, 315–318 (1988). https://doi.org/10.1007/BF00714474
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DOI: https://doi.org/10.1007/BF00714474