On invertibility and zero-augmentability of N-gon orders (Q1262881)

The author considers classes of finite partially ordered sets \((X,<)\) representable in R (R denotes a collection of closed and connected regions in the plane) by proper inclusion for which there is a map f: \(X\to R\) such that for all \(x,y\in X\), \(x<y\Leftrightarrow f(x)<f(y)\). It is proved that certain classes of posets that have representations by N- gons in the plane are neither invertible nor zero-augmentable.