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:

http://math.sfsu.edu/federico/Clase/EC/LectureNotes/ardilaec20.pdf

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?

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