Angle orders
A finite poset is an angle order if its points can be mapped into angular regions in the plane so that x precedes y in the poset precisely when the region for x is properly included in the region for y. Main results: 1. Every poset with dimension 4 or less is an angle order. 2. Every interval order is an angle order. 3. The fact that some angle orders must have an angular region less than 180\(\circ\) (or more than 180\(\circ)\) implies the existence of posets that are not angle orders. Finally, the authors discuss questions about the smallest poset that is not an angle order and other problems, including whether there are dimension 5 posets that are not angle orders.
scientific article; zbMATH DE number 3889591