1. In Lecture 20 I sketched MacMahon’s proof for the enumeration of plane partitions, reducing it to an evaluation of a determinant built from one row of Pascal’s triangle. See the bottom of pg 90:
Was anyone able to prove this formula?
2. Play around with Dodgson’s condensation; can you use it to prove interesting determinantal formulas? For example, can you compute Vandermonde’s determinant with it? More interesting examples?