Readings and Lecture Notes

Readings are Assigned in the Recommended Texts:

[EC1] = Buy at Amazon Stanley, Richard P. Enumerative Combinatorics. Vol. 1. Cambridge, UK: Cambridge University Press, 1997. ISBN: 9780521553094.

[EC2] = Buy at Amazon ———. Enumerative Combinatorics. Vol. 2. Cambridge, UK: Cambridge University Press, 2001. ISBN: 9780521789875.

[TAC] = "Topics in Algebraic Combinatorics." by Richard Stanley (Notes available online (This resource may not render correctly in a screen reader.PDF).)

Supplemental lecture notes are provided for some of the lectures.

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 (This resource may not render correctly in a screen reader.PDF)