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.