CS0901: Combinatorics

Shanghai Jiao Tong University, Fall 2024

 

Course Information

InstructorKuan Yang
Lecture timesWednesday 18:00 - 20:30     (Week 1 - 16)
LocationMiddle Hall 106 (中院 106)
Teaching assistant(s)Zhidan Li (李至丹)
Office hoursTo be determined

 

News and Announcements

 

Textbook and References

 

Syllabus

  1. Counting
  1. Structures
  1. Existence and Extremal Problems
  1. The Probabilistic Method
  1. Linear Algebraic Methods

 

Lecture Schedule

WeekDateTopicsLecture notes
209/25Introduction, the twelvefold way, binomial coefficients,
double counting, combinatorial identities, Catalan numbers
Lecture 01
410/09Generating functionsLecture 02
510/16Principle of Inclusion and exclusion, Möbius inversionLecture 03
610/23Posets, chains and antichains, Möbius inversion on posetsLecture 04
710/30Graph theory basicsLecture 05
811/06Colorings, bipartite graph matchingsLecture 06
911/13Pigeonhole principle, happy ending problem, Ramsey theoryLecture 07
1011/20Extremal graph theory, Zarankiewicz’s problemLecture 08
1111/27Extremal systems in discrete geometry, extremal set familiesLecture 09
1212/04Basic probabilistic arguments, linearity of expectationLecture 10
1312/11Alterations, Markov's inequality, second moment methodLecture 11
1412/18Lovász local lemma, Moser's constructive proofLecture 12
1512/25Dimensions of linear spaces, eigenvalues of graphsLecture 13