P198: Enumeration of all $k$-cardinarity ideals of a $w$-element poset

P198: Enumeration of all $k$-cardinarity ideals of a $w$-element poset
Input:
An integer $k$ and a poset $P$ with $w$ element, where $k \le w$.
Output:
All $k$-cardinarity ideals of $P$.
Complexity:
$O(Nw^3)$ total time.
Comment:
$N$ is the number of ideals.
Reference:
[Wild2013] (Bibtex)