ABSTRACT
We survey three important research themes involving dimension for partially ordered sets (posets). In each case, there are analogous results involving chromatic number for graphs. These themes have been chosen to highlight recent research on the combinatorics of posets and to illustrate the broad range of connections with other areas of combinatorial mathematics. All of the major results are from papers published since 2015. We outline proofs for these results, and this approach yields a number of good exercises for students. Each exercise comes with a degree of difficulty scored by one chili pepper 🌶 (easy) to three chili peppers (really challenging). We also include comments on open problems for future research.
