**Discrete Mathematics and Optimization Seminar**

** JONATHAN FARLEY**

* University of the West Indies *

Tuesday April 3rd at 4pm

* Burnside 1205*

**Title. *** Distributive Lattices of Small Width: A problem from Stanley's Enumerative Combinatorics.*

**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 *\sum f*_{k}(n) x^{n}? 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.