## 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) |