Abstract
In Richard P. Stanley's 1986 text, Enumerative Combinatorics, the following problem is posed: Fix a natural number k. Consider the posets P of cardinality n such that, for 0 < i < n , P has exactly k order ideals (down-sets) of cardinality i. Let f k ( n ) be the number of such posets. What is the generating function ∑ f 3 ( n ) x n ? In this paper, the problem is solved.
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