Outline

1.

Counting

(a)

Permutations and Combinations

(b)

Binomial Coefficients

(c)

Inclusion-Exclusion

(d)

Generating Functions

2.

Graphs

(a)

Trees

(b)

Matchings and Systems of Distinct Representatives

(c)

Connectivity

(d)

Chromatic number, Clique Number and Independence Number.

(e)

Planar Graphs

3.

Designs

(a)

Steiner Triple Systems and block designs.

(b)

Orthogonal Latin Squares, Transversal Designs and Orthogonal Arrays

(c)

Projective Planes

(d)

Pairwise Balanced Designs

References:

R.A. Brualdi, Introductory Combinatorics, Prentice Hall, 1999.

H.J. Ryser, Combinatorial Mathematics, Mathematical Association of America, Carus Mathematical Monograph, Number 14, 1963.

D.B. West, Introduction to Graph Theory, Prentice Hall, 2000.

A. Tucker, Applied Combinatorics, John Wiley & Sons, Inc.