@article {IOPORT.05639009,
    author       = {Farley, Jonathan David and Klippenstine, Ryan},
    title        = {Distributive lattices of small width. II: A problem from Stanley's 1986 text {\sl Enumerative combinatorics}.},
    year         = {2009},
    journal      = {Journal of Combinatorial Theory. Series A},
    volume       = {116},
    number       = {6},
    issn         = {0097-3165},
    pages        = {1097-1119},
    publisher    = {Elsevier Science (Academic Press), San Diego, CA},
    doi          = {10.1016/j.jcta.2008.08.007},
    abstract     = {In this paper, the authors solve a problem that {\it R. P. Stanley} posed in his classic text [Enumerative combinatorics. Volume I. Monterey, CA: Wadsworth \& Brooks/Cole Advanced Books \& Software (1986; Zbl 0608.05001)]. Stanley's problem is the following: Fix a natural number $k$. Consider the posets $P$ of cardinality $n$ such that, for $0 < i < n$, $P$ has exactly $k$ ordered ideals of cardinality $i$. If ${f_k}(n)$ is the number of such posets, what is the generating function $\sum {f_3}(n)x^n$? In this paper, the authors investigate this problem, producing a system of recurrence relations that enumerate the isomorphism classes of these lattices. They also derive a generating function from this system of recurrences.},
    reviewer     = {Renata Majovsk\'a (Horn\'{\i} Such\'a)},
    identifier   = {05639009},
}