Finite distributive lattices and the splitting property
by
Bill Sands
University of Calgary
Coauthors: Dwight Duffus (Emory University)

A finite partially ordered set P has the splitting property if every maximal antichain splits into two parts so that P is the union of the upset of one part and the downset of the other. Ahlswede, Erdos and Graham introduced this notion, and proved that every finite Boolean lattice has the splitting property. We will show that there are exactly three other finite distributive lattices with the splitting property.

We will also introduce the notion of splitting number, which measures how close a finite distributive lattice is to having the splitting property. We give what we know of this concept, and state some interesting problems.

Date received: April 17, 2001