The many faces of circle orders

A finite partially ordered set P is called a circle order if one can assign to each x P a circular disk C_x so that xy iff C_xC_y. It is interesting to observe that many other classes of posets, such as space-time orders, parabola orders, the Loewner order for 2×2 Hermitian matrices, etc. turn out to be exactly circle orders (or their higher dimensional analogues). We give a global proof for these equivalences.Research supported in part by the Office of Naval Research, the Air Force Office of Scientific Research and by DIMACS.