Interval orders and circle orders
A finite partially ordered set \((X,<_ 0)\) is said to be an interval order if each \(x\in X\) can be mapped into a bounded closed real interval I(x) so that, for all \(x,y\in X\), \(x<_ 0y\Leftrightarrow \sup I(x)<\inf I(y)\); it is said to be a circle order if each \(x\in X\) can be mapped into a circular disk \(C(x)\subseteq R^ 2\) so that, for all \(x,y\in X\), \(x<_ 0\Leftrightarrow C(x)\subset C(y)\). This paper proves that every finite interval order is a circle order.
scientific article; zbMATH DE number 4083688