Combinatorics Fall 2012
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Combinatorics – Fall 2012
Skip to second half of course

Tuesday, August 28 (pdf of Notes pages 0–10) 

  • Material from Section 1.1 and more
  • Course Introduction

Thursday, August 30 (pdf of Notes pages 11–24) 

  • Material from Sections 1.1 and 1.2
  • Simple Counting
  • Multiplication Principle
  • Examples

Tuesday, September 4 (pdf of Notes pages 25–37) 

  • Material from Sections 1.1 - 1.3
  • Counting pitfalls
  • Overcounting, Counting the complement
  • Bijections

Thursday, September 6 (pdf of Notes pages 38–44) 

  • Material from Section 1.4

Tuesday, September 11 (pdf of Notes pages 45–56) 

  • Material from Sections 2.1 and 2.2
  • Equivalence classes
  • Counting using symmetry
  • Counting distributions

Thursday, September 13

  • Discussion of Homework 2

Thursday, September 20 (pdf of Notes pages 57–60) 

  • Material from Sections 2.1-2.3
  • More distributions
  • The binomial theorem
  • Combinatorial proofs
  • Worksheet on combinatorial proofs

Thursday, September 28 (pdf of Notes pages 61–72) 

  • Material from Sections 2.3, 2.4, and Chapter 3
  • Combinatorial proofs
  • Worksheet on combinatorial proofs

Tuesday, October 2 (pdf of Notes pages 73–76) 

  • Material from Section 4.2
  • Domino-square interpretations

Thursday, October 4

  • Discussion of Homework 4

Tuesday, October 9 (pdf of Notes pages 77–85) 

  • Material not in the book
  • Combinatorial statistics
  • Permutation representations
  • descent, inversion, major statistic

Thursday, October 11

  • Question and Answer Day

Tuesday, October 16

  • Exam 1

Thursday, October 18 and Tuesday, October 23 (pdf of Notes pages 86–95) 

  • Material from Sections 3.3
  • Introduction to generating functions
  • Generating function manipulations
  • Generating function worksheet

Thursday, October 25 (pdf of Notes pages 96–101) 

  • Material from Section 3.5
  • Solving recurrence relations
  • Fibonacci generating function

Tuesday, November 6

  • Discussion of Homework 7

Thursday, November 8 (pdf of Notes pages 102–110)  (These are the same notes that were posted before the storm.)

  • Material from Sections 2.4, 3.4, and 4.4
  • Integer partitions
  • Integer partition bijections

Tuesday, November 13 (pdf of Notes pages 111–116)  AND (117–118) 

  • Material from Section 3.4 PLUS additional material
  • Products of generating functions
  • Compositions of generating functions
  • And their combinatorial interpretations

Thursday, November 15 (pdf of Notes pages 119–127) 

  • Material from Section 4.1 PLUS additional material
  • Catalan numbers
  • Catalan number interpretations
  • Catalan number generating function
  • (link to Stanley's Catalan Interpretations)

Tuesday, November 20 (pdf of Notes pages 128–133) 

  • Material from Section 6.2
  • Graph Theory definitions
  • Labeled trees
  • Binary trees

Tuesday, November 27 (pdf of Notes pages 134–139) 

  • Material about q-analogs
  • q-factorials, q-Binomial coefficients
  • Multivariate generating functions
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Christopher HanusaQueens CollegeMathematics Department.