Readings are Assigned in the Recommended Texts:
[EC1] = 
Stanley, Richard P. Enumerative Combinatorics. Vol. 1. Cambridge, UK: Cambridge University Press, 1997. ISBN: 9780521553094.
[EC2] = ———. Enumerative Combinatorics. Vol. 2. Cambridge, UK: Cambridge University Press, 2001. ISBN: 9780521789875.
[TAC] = "Topics in Algebraic Combinatorics." by Richard Stanley (Notes available online (
PDF).)
Supplemental lecture notes are provided for some of the lectures.
| LEC # | TOPICS | READINGS | LECTURE NOTES |
|---|---|---|---|
| 1 | Introduction to course, walks on graphs, rational generating functions and Fibonacci numbers | [EC1] Chapter 4 | (PDF) |
| 2 | Walks on graphs II: walks on complete graphs and cubes | [TAC] Section 1 | |
| 3 | Walks on graphs III: the Radon transform | [TAC] Section 2 | |
| 4 | Random walks, the Perron-Frobenius theorem | [TAC] Section 3 | |
| 5 | Introduction to partially ordered sets and the Boolean poset | [TAC] Section 4 | |
| 6 | Partially ordered sets II: Dilworth's and Sperner's theorem | [TAC] Section 4 | (PDF) |
| 7 | Partially ordered sets III: the Mobius function | [EC1] Chapter 3 | (PDF) |
| 8 | Group actions on Boolean algebras | [TAC] Section 5 | |
| 9 | Group actions on Boolean algebras II: proof of the Sperner property | [TAC] Sections 4 and 5 | |
| 10 | Introduction to partitions and two proofs of Euler's theorem | (PDF) | |
| 11 | Partitions II : Euler Pentagonal theorem and other identities | (PDF) | |
| 12 | Partitions in a box, q-binomial coefficients, and introduction to Young tableaux | [TAC] Section 6 | |
| 13 | Standard Young tableaux and the Hook length formula | [TAC] Section 8 | |
| 14 | The Hook length formula II, and introduction to the RSK algorithm | [TAC] Section 8 (including section 8 appendix) | |
| 15 | Proof of Schensted's theorem | (PDF) | |
| 16 | Catalan numbers | [EC2]: Chapter 6 | |
| In-class quiz #1 | |||
| 17 | Counting Hasse walks in Young's lattice | [TAC] Section 8 | |
| 18 | An introduction to symmetric functions | [EC2] Chapter 7 | (PDF) |
| 19 | Symmetric functions II | [EC2] Chapter 7 | (PDF) |
| 20 | Polya theory I | [TAC] Section 7 | |
| 21 | Polya theory II | [TAC] Section 7 | |
| 22 | Polya theory III, intro to exponential generating functions | [TAC] Section 7 | (PDF) |
| 23 | Exponential generating functions and tree enumeration | [EC2] Chapter 5 | (PDF) |
| 24 | Tree enumeration II | [EC2] Chapter 5 | (PDF) |
| 25 | Matrix tree theorem | [TAC] Section 9 | |
| 26 | Matrix tree theorem II and Eulerian tours | [TAC] Section 9 and 10 | |
| 27 | Eulerian tours II | [TAC] Section 10 | (PDF) |
| In-class quiz #2 | |||
| 28 | Binary de Brujin sequences | [TAC] Section 10 | |
| 29 | Chip firing games I | (PDF) | |
| 30 | Chip firing games II: the critical group | (PDF) | |
| 31 | Chip firing games III: proof of uniqueness | (PDF) | |
| 32 | Perfect matchings and Domino tilings | (PDF) | |
| 33 | Perfect matchings and Domino tilings II | ||
| 34 | Pfaffians and matching enumeration | ||
| 35 | Aztec diamonds | ||
| 36 | Aztec diamonds II; Lattice path enumeration | ||
| 37 | Lattice path enumeration II | Benjamin, A.T., and N. Cameron "Counting on Determinants" available online (PDF) |