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Line directionality of orders |
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| Authors: | Vincent Bouchitté Roland Jégou Jean-Xavier Rampon |
| Institution: | (1) LIP-IMAG, CNRS URA 1398, Ecole Normale Supérieure de Lyon, 46, allée d'Italie, 69364 Lyon Cedex 07, France;(2) Dept. Informatique Appliquée, E.N.S. des Mines de Saint-Etienne, 158, Cours Fauriel, 42023 Saint-Etienne Cedex 2, France;(3) IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France |
| 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. |
| Keywords: | Primary 06A06 secondary 52A37 |
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