Abstract
Some orders can be represented by translating convex figures in the plane. It is proved thatN-free and interval orders admit such representations with an unbounded number of directions. Weak orders, tree-like orders and two-dimensional orders of height one are shown to be two- directional. In all cases line segments can be used as convex sets.
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Bouchitté, V., Jégou, R. & Rampon, JX. Line directionality of orders. Order 10, 17–30 (1993). https://doi.org/10.1007/BF01108705
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DOI: https://doi.org/10.1007/BF01108705