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