Georgia Institute of Technology College of Sciences

In the paper "On the Size of Maximal Chains and the Number of Pariwise Disjoint Maximal Antichains" Duffus and Sands proved the following:If P is a poset whose maximal chain lengths lie in the interval [n,n+(n-2)/(k-2)] for some n>=k>=3 then there exist k disjoint maximal antichains in P. Furthermore this interval is tight. At the end of the paper they conjecture whether the dual statement is true (swap the words chain and antichain in the theorem). In this talk I will prove the dual and if time allows I will show a stronger version of both theorems.