The top ten theorems on partially ordered sets
by
W. T. (Tom) Trotter
Arizona State University

A few years ago, I gave an impromptu lecture with the title ``The Top Five Theorems on Posets.'' It was a light hearted affair, but in retrospect it got the audience to thinking about whether they agreed or disagreed with my choices, and it certainly caused me to think more deeply about the most significant threads for research on partially ordered sets. So in this talk, I propose to revisit this theme, expanding from five to ten to give me a little more room. Some choices are obvious. You have to include Dilworth's chain partitioning theorem and Sperner's lemma giving the width of the subset lattice. Here are three more: (1) Schnyder's theorem testing planarity for graphs in terms of the dimension of the incidence poset; (2) Canfield's disproof of Rota's cross-cut conjecture for the partition lattice; and (3) Brightwell, Felsner and Trotter's improvement to the Kahn/Saks theorem on balancing pairs. So what are the other five?

Date received: April 18, 2001