Abstract
A poset is a circle order if its points can be mapped into circular disks in the plane so that x<y in the poset precisely when x's circular disk is properly included in y's; the poset is an angle order if its points can be mapped into unbounded angular regions that preserve < by proper inclusion. It is well known that many finite angle orders are not circle orders, but has been open as to whether every finite circle order is an angle order. This paper proves that there are finite circle orders that are not angle orders.
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Communicated by I. Rival
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Fishburn, P.C. Circle orders and angle orders. Order 6, 39–47 (1989). https://doi.org/10.1007/BF00341635
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DOI: https://doi.org/10.1007/BF00341635