Math 580B: Topics in Combinatorial Analysis
Introduction to Combinatorics
Meeting time and place:
MWF 3:30-4:30 in LN-2201.
This is an introduction to basic concepts of combinatorics, mostly excluding graph theory (a separate course). We will study various chapters from
J.H. van Lint and R.W. Wilson,
A Course in Combinatorics, second edition (2001),
Cambridge University Press.
The class is conducted mainly through student lectures on short assigned material from the book.
- Ch. 1: Graphs. (This is for a quick review and to learn their terminology.)
- Ch. 5: Systems of distinct representatives.
- Ch. 6: Dilworth's theorem and extremal set theory.
- Ch. 10: The principle of inclusion and exclusion; inversion formulae.
- Ch. 13: Elementary counting; Stirling numbers.
- Ch. 14: Recursions and generating functions.
- Ch. 15: Partitions.
- Ch. 17: Latin squares. (To Theorem 15.1; also the Dinitz conjecture, pp. 193-4.)
- Ch. 19: Designs.
- Ch. 22: Orthogonal Latin squares. (To Problem 22C. Omit the proofs of Theorems 22.6-8; omit the harder problems. In class I will explain k-nets, which the authors call (n,k)-nets.)
- Ch. 23: Projective and combinatorial geometries.
- Ch. 24: Gaussian numbers and q-analogues.
- Ch. 25: Lattices and Möbius inversion.
- (We do not have time for: Ch. 26: Combinatorial designs and projective geometries.)
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