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 x is an element ofX so that x <y precisely when x's distinguished point precedes y's interval, and x's interval precedes y's distinguished point. For each \X \ less than or equal to9, 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).