Combinatorics Fall 2011
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Combinatorics – Fall 2011

Monday, August 29 (pdf of Notes pages 0–18)  (Additional notes from class)  

  • Material from Section 1.1 and more
  • Course Introduction

Wednesday, August 31 (pdf of Notes pages 19–24) 

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

Wednesday, September 7 (pdf of Notes pages 25–31) 

  • Material from Sections 1.1 and 1.2
  • Counting pitfalls
  • Counting the complement

Monday, September 12 (No new notes.)

  • Material from Section 1.3
  • Bijections
  • Functions, Inverse function
  • Examples of bijections
Wednesday, September 14 (pdf of Notes pages 32–38) 

Monday, September 19

  • Discussion of Homework 2.

Wednesday, September 21 (pdf of Notes pages 39–42) 

  • Material from Sections 1.4, 2.1, and 2.2
  • Discussion of Homework 2-5.
  • The equivalence principle

Monday, September 26 (pdf of Notes pages 43–47) 

Monday, October 3 (pdf of Notes pages 48–50) 

  • Material from Sections 2.1 and 2.2
  • Distributions
  • The Binomial Theorem
  • Counting integral solutions

Wednesday, October 5

  • Discussion of Homework 4.

Wednesday, October 12 (pdf of Notes pages 51–56) 

  • Material from Sections 2.3 and 2.4
  • Set Partitions
  • Stirling Numbers (of the second kind)
  • Integer Partitions
  • Partition Numbers

Monday, October 17

  • Question and Answer Session

Wednesday, October 19

  • Exam 1

Monday, October 24 (pdf of Notes pages 57–65) 

  • Material from Section 3.1
  • Principle of Inclusion/Exclusion
Wednesday, October 26 (pdf of Notes pages 66)  AND (pdf of Notes pages 67–78) 

  • Material from Sections 3.1 and 3.3
  • A formula for Stirling numbers
  • Generating functions
Monday, October 31 (No additional Notes)

  • Material from Sections 3.3 and 3.4
  • Generating function examples
  • Generating function worksheet

Wednesday, November 2

  • Discussion of Homework 6

Monday, November 7 (pdf of Notes pages 79–82) 

  • Material from Section 3.5
  • Solving recurrence relations using generating functions

Wednesday, November 9 (pdf of Notes pages 83–90) 

  • Material from Sections 2.4,3.4,4.4
  • Generating functions and partitions

Monday, November 14 (pdf of Notes pages 91–95) 

  • Material from Sections 4.2 and 4.4
  • Partition identities and bijections
  • Standard Young Tableaux
  • Square-Domino tilings

Wednesday, November 16 (pdf of Notes pages 96–104) 

  • Material from Sections 4.1 and Supplemental Material
  • Catalan numbers
  • Catalan interpretations

Monday, November 21 (pdf of Notes pages 105–110) 

  • Material from Section 6.2
  • Graphs, Trees
  • Counting Labeled Trees
  • Counting Binary Trees

Wednesday, November 23

  • No Class; Happy Thanksgiving!

Monday, November 28

  • Discussion of Homework 8

Wednesday, November 30 (pdf of Notes pages 111-123) 

  • Research in Core Partitions

Monday, December 5

  • Question and Answer Session

Wednesday, December 7

  • Exam 2

Monday, December 12

  • Poster Work Day
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Christopher HanusaQueens CollegeMathematics Department.