Interval orders based on arbitrary ordered sets Original Research Article

In general, an interval order is defined to be an ordered set which has an interval representation on a linearly ordered set, the real numbers for example. Bogart et al. (1991) generalized this concept and allowed the underlying set to be weakly ordered. They found a necessary and sufficient condition for an ordered set to be an interval order based on a weak order as well as a characterization for this class of ordered sets by 4 forbidden suborders. In this paper interval orders based on further classes of ordered sets are investigated. Hereby, we concentrate on classes characterized by one forbidden suborder, such as series-parallel orders and interval orders. Furthermore, we analyse connections between order dimension and interval dimension.