author : Peter J. Cameron

Contents:

1. What is combinatorics?
2. On numbers and counting
   • induction
3. Subsets, partitions, permutations
   • binomial theorem • Pascal's triangle • Cayley's theorem • Bell numbers
4. Recurrence relations and generating functions
   • Fibonacci numbers • Catalan numbers
5. The principle of inclusion and exclusion
   • Stirling numbers
6. Latin squares and SDRs
   • Hall's theorem • quasigroups
7. Extremal set theory
   • Sperner families • de Bruijn-Erdos theorem
8. Steiner triple systems
9. Finite geometry
   • Gaussian coefficients • projective geometry • Pappus' theorem
10. Ramsey's theorem
    • pigeonhole principle (Dirichlet)
11. Graphs
    • trees and forests • minimal spanning trees • Eulerian graphs • bridges of Konigsberg • Gray codes • digraphs • networks • Moore graphs
12. Posets, lattices, and matroids
    • chains and antichains • Arrow's theorem
13. More on partitions and permutations
    • conjugacy classes • Jacobi's identity • tableaux
14. Automorphism groups and permutation groups
    • orbits
15. Enumeration under group action
    • direct and wreath products
16. Designs
    • Fisher's inequality • Hadamard matrices
17. Error-correcting codes
    • Shannon's theorem • bounds • Hamming codes
18. Graph colourings
19. The infinite
    • Zorn's lemma • Erdos-Renyi theorem
20. Where to from here?
    • computational complexity