| Lec # | Topics | Key dates |
|---|---|---|
| 1 | Catalan Numbers | |
| 2 | Pattern Avoidance in Permutations, Young Tableaux, Schensted Correspondence, Longest Increasing Subsequences | |
| 3 | The Hooklength Formula Random Hook Walks A "Hooklength Formula" for Increasing Trees | |
| 4 | q-analogues, q-binomial Coefficients, q-factorials | |
| 5 | Symmetric Group, Statistics on Permutations, Inversions and Major Index | |
| 6 | Posets, Lattices, Distributive Lattices, Young's Lattice, Differential Posets | |
| 7 | Up and Down Operators, Unimodality of Gaussian Coefficients | |
| 8 | Sperner's and Dilworth's Theorems | Problem set 1 due |
| 9 | De Bruijn Sequences | |
| 10 | Partitions: Euler's Pentagonal Theorem, Jacobi Triple Product | |
| 11 | Lindstrom Lemma (Gessel-Viennot Method) Exponential Formula | |
| 12 | Weighted Lattice Paths and Continued Fractions | Problem set 2 due |
| 13 | Review of Problem Set 1 | |
| 14 | Review of Problem Set 2 | |
| 15 | Cayley's Formula, Prufer's Codes, Egecioglu and Remmel's Bijection | |
| 16 | Spanning Trees, Matrix-Tree Theorem, Directed Matrix-Tree Theorem | Problem set 3 due |
| 17 | Electrical Networks | Problem set 4 due |
| 18 | Review of Problem Set 3 | |
| 19 | BEST Theorem Permutohedra, Newton Polytopes, Zonotopes | |
| 20 | Domino Tilings of Rectangles | |
| 21 | Birkhoff Polytope and Hall's Marriage Theorem | |
| 22 | Pfaffians and Matching Enumeration, Ising Model | |
| 23 | Plane Partitions, Rhombus Tilings of Hexagon, Pseudoline Arrangements | |
| 24 | Review of Problem Set 4 | |
| 25 | Eulerian Numbers and Hypersimplices | |
| 26 | What Next? |