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COMBINATORIAL THEORY

Instructor: Prof. Gregory M. Constantine; 509 TY, 624-8308

Text: Constantine's "Combinatorial Theory and Statistical Design"

Office hours: Tu, Th 4 - 5:15 and by appointment

Grades: Homework 30%, Exam 1 20%, Exam 2 20%, Final exam 30%

Homework assigned during a week is due Tuesday of the following week.

COURSE OUTLINE

Week 1 Binomial and Stirling numbers

Week 2 Generating functions, Kirchhoff's tree enumerating function

Week 3 Leibniz's formula, Faa di Bruno's formula

Week 4 Finite fields, Gaussian polynomials

Week 5 Inversion: Lagrange, Mobius; Exam 1 (Th)

Week 6 Projective and affine geometries

Week 7 Finite projective planes, Symmetric 2-designs

Week 8 The Bruck-Ryser-Chowla theorem

Week 9 Hadamard matrices, t-designs

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Week 10 Symmetry groups; Exam 2

Week 11 More on t-designs

Week 12 Association schemes

Week 13 Examples and discussion

Week 14 Connections to Coding theory and Statistical design

Week 15 Connections to Computer science and Probability

Week 16 Review; Final exam

Recommended reading:

Stanley's book on "Generating functions"

MacMahon's two volumes on "Combinatory Analysis"

Cameron and Van Lint's "Graphs, Codes, and Designs"

Sloane and MacWilliams volumes on "Error correcting codes"

Hughes' book on Designs

Lander's London Math Society volume on "Symmetric designs"

Enjoy!