On the fixed point property for \((3 + 1)\)-free ordered sets (Q651421)

The authors prove the theorem that if a finite \(\left( {3 + 1} \right)\)-free ordered set of height two has the fixed-point property, then it is dismantlable by irreducibles. They give an example of a finite \(\left( {3 + 1} \right)\)-free ordered set of height three with fixed-point property and no irreducible elements and characterize the minimal automorphic ordered sets which are, respectively, \(\left( {3 + 1} \right)\)-free, \(\left( {2 + 2} \right)\)-free and \(N \)-free.