Fixed Point On Partially Ordered Sets

This paper is mainly focused on the open question: Characterize those (finite) ordered sets that have the fixed point property. As the basis for further discussion, basic concepts and properties are introduced in the first part. Afterwards, a new concept: generalized irreducible element is given and the relation among retract, automorphic poset, crown and fixed point property is studied. Finally, we discuss the fixed point property on lattice and dual fixed point property.