A partial order ideal 
of a partial order 
is a subset of 
such that if 
and 
, then 
. This is the combinatorial convention, which includes
the empty set (Stanley 2011, p. 281). In other
order-theoretic conventions, an ideal is additionally required to be nonempty and
a directed set (Abramsky and Jung 1994, Definition 2.1.8).
For 
disjoint chains in which the 
th chain contains 
elements, there are 
ideals in the combinatorial sense.
The number of such ideals of an 
-element fence poset is the
Fibonacci number 
.
