|Discrete Mathematics and Optimization Seminar
University of the West Indies
Tuesday April 3rd at 4pm
Title. Distributive Lattices of Small Width: A problem from Stanley's Enumerative Combinatorics.
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 fk(n) be the number
of such posets. What is the generating function \sum fk(n) xn? I will give a solution to
this problem (joint work with Ryan Klippenstine.) I will also relate this to a problem of
Ivo Rosenberg (University of Montreal) from the 1981 Banff Conference on Ordered Sets.