Georgia Institute of Technology College of Sciences

Answering a question of R. Stanley, we show that for each t ≥1, there is a least positive integer f(t) so that a planar poset with t minimal elements has dimension at most f(t). In particular, we show that f(t) ≤ 2t + 1 and that this inequality is tight for t=1 and t=2. For larger values of t, we can only show that f(t) ≥ t+3. This research is joint work with Georgia Tech graduate student Ruidong Wang.