Counting Split Interval Orders

A poset (X,) is a split interval order (a.k.a. unit bitolerance order, proper bitolerance order) if a real interval and a distinguished point in that interval can be assigned to each xX so that xy precisely when x's distinguished point precedes y's interval, and x's interval precedes y's distinguished point. For each |X|9, we count the split interval orders and identify all posets that are minimal forbidden posets for split interval orders. The paper is a companion to Counting Split Semiorders by Fishburn and Reeds (this issue).