About posets for which no lower cover or no upper cover has the fixed point property [article]

Frank a Campo
2022 arXiv   pre-print
For a finite non-empty set X, let 𝔓(X) denote the set of all posets with carrier X, ordered by inclusion of their partial order relations. We investigate properties of posets P ∈𝔓(X) for which no lower cover or no upper cover in 𝔓(X) has the fixed point property. We derive two conditions, one of them sufficient for that no lower cover of P has the fixed point property, the other one sufficient for that no upper cover of P has the fixed point property, and we apply these results on several types of posets.
arXiv:2109.09431v2 fatcat:ejfvrloy3zeqpboff4e4bfmovq