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A short proof that N 3 is not a circle containment order

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Abstract

A partially ordered set P is called a circle containment order provided one can assign to each x∈P a circle C x so that \(x \leqslant y \Leftrightarrow C_x \subseteq C_y \). We show that the infinite three-dimensional poset N 3 is not a circle containment order and note that it is still unknown whether or not [n]3 is such an order for arbitrarily large n.

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Reference

  1. E. R. Scheinerman and J. C. Wierman, 1987, On circle containment orders, preprint.

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Authors and Affiliations

  1. Department of Mathematics, SUNY, 11794, Stony Brook, NY, U.S.A.

    Glenn H. Hurlbert

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  1. Glenn H. Hurlbert
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Communicated by I. Rival

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Hurlbert, G.H. A short proof that N 3 is not a circle containment order. Order 5, 235–237 (1988). https://doi.org/10.1007/BF00354890

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  • DOI: https://doi.org/10.1007/BF00354890

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