A poset power 
is the partially ordered set of isotone
maps from a partially ordered set 
to a partially
ordered set 
, ordered pointwise. Thus 
means 
for every 
(Farley and Grätzer 2026). The partial
order on the maps, rather than their composition, is the structure used in this
definition.
Farley and Grätzer (2026) proved that, for finite nonempty partially ordered sets 
and 
, an order
isomorphism 
implies an order isomorphism 
.
This resolves Duffus's reconstruction question for poset powers (Farley and Grätzer
2026). It differs from poset reconstruction
from one-element-deletion decks. The nonempty hypothesis matters, since the empty
partially ordered set and the one-element
partially ordered set both have a one-element
self-power.
Problem for Finite Ordered Sets." 14 Oct 2026.