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Interval orders and circle orders

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Abstract

A finite poset is an interval order if its point can be mapped into real intervals so that x<y in the poset precisely when x's interval lies wholly to the left of y's; the poset is a circle order if its points can be mapped into circular disks in the plane so that x<y precisely when x's circular disk is properly included in y's. This note proves that every finite interval order is a circle order.

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  1. AT & T Bell Laboratories, 07974, Murray Hill, NJ, U.S.A.

    P. C. Fishburn

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  1. P. C. Fishburn
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Communicated by I. Rival

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Fishburn, P.C. Interval orders and circle orders. Order 5, 225–234 (1988). https://doi.org/10.1007/BF00354889

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  • DOI: https://doi.org/10.1007/BF00354889

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