| L1 |
Introduction to course, walks on graphs, rational generating functions and Fibonacci numbers |
|
| L2 |
Walks on graphs II: walks on complete graphs and cubes |
|
| L3 |
Walks on graphs III: the Radon transform |
|
| L4 |
Random walks, the Perron-Frobenius theorem |
Homework 1 due |
| L5 |
Introduction to partially ordered sets and the Boolean poset |
|
| L6 |
Partially ordered sets II: Dilworth's and Sperner's theorem |
|
| L7 |
Partially ordered sets III: the Mobius function |
Homework 2 due |
| L8 |
Group actions on Boolean algebras |
|
| L9 |
Group actions on Boolean algebras II: proof of the Sperner property |
|
| L10 |
Introduction to partitions and two proofs of Euler's theorem |
Homework 3 due |
| L11 |
Partitions II: Euler Pentagonal theorem and other identities |
|
| L12 |
Partitions in a box, q-binomial coefficients, and introduction to Young tableaux |
|
| L13 |
Standard Young tableaux and the Hook length formula |
Homework 4 due |
| L14 |
The Hook length formula II, and introduction to the RSK algorithm |
|
| L15 |
Proof of Schensted's theorem |
|
| L16 |
Catalan numbers |
Homework 5 due |
| E1 |
In-class quiz 1 |
|
| L17 |
Counting Hasse walks in Young's lattice |
|
| L18 |
An introduction to symmetric functions |
|
| L19 |
Symmetric functions II |
Homework 6 due |
| L20 |
Polya theory I |
|
| L21 |
Polya theory II |
Homework 7 due |
| L22 |
Polya theory III, intro to exponential generating functions |
|
| L23 |
Exponential generating functions and tree enumeration |
|
| L24 |
Tree enumeration II |
Homework 8 due |
| L25 |
Matrix tree theorem |
|
| L26 |
Matrix tree theorem II and Eulerian tours |
|
| L27 |
Eulerian tours II |
Homework 9 due |
| E2 |
In-class quiz 2 |
|
| L28 |
Binary de Brujin sequences |
|
| L29 |
Chip firing games I |
|
| L30 |
Chip firing games II: the critical group |
|
| L31 |
Chip firing games III: proof of uniqueness |
|
| L32 |
Perfect matchings and Domino tilings |
Homework 10 due |
| L33 |
Perfect matchings and Domino tilings II |
|
| L34 |
Pfaffians and matching enumeration |
|
| L35 |
Aztec diamonds |
|
| L36 |
Aztec diamonds II; Lattice path enumeration |
|
| L37 |
Lattice path enumeration II |
|
