An ideal 
of a partial order 
is a subset of the elements of 
which satisfy the property that if 
and 
, then 
. For 
disjoint chains in which the 
th chain contains 
elements, there are 
ideals. The number of ideals of a 
-element fence
poset is the Fibonacci number 
.
Partial Order Ideal
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References
Ruskey, F. "Information on Ideals of Partially Ordered Sets." http://www.theory.csc.uvic.ca/~cos/inf/pose/Ideals.html.Steiner, G. "An Algorithm to Generate the Ideals of a Partial Order." Operat. Res. Let. 5, 317-320, 1986.Referenced on Wolfram|Alpha
Partial Order IdealCite this as:
Weisstein, Eric W. "Partial Order Ideal." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PartialOrderIdeal.html