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 .
References
Ruskey, F. ``Information on Ideals of Partially Ordered Sets.''
http://sue.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.