Forbidden retracts for finite ordered sets of width at most four Original Research Article

The relationship between the fixed point property and forbidden retracts associated with a forgetful functor is formulated. Finite ordered sets of width at most four with fixed point free automorphisms are described. Linear time algorithms for deciding whether a finite ordered set of width two has the fixed point property and whether a finite ordered set of width at most three has a fixed point free automorphism are presented.