MAD 6209: Enumerative Combinatorics
Time: MW 5:30 –
6:50 pm. Maybe we can change that …
Recommended text book: Enumerative Combinatorics,
Volume 1, by Richard Stanley. Volume 2 is also strongly recommended, of
course.
Goal: Learn some general
methods, enjoy a wide
range of example, and study at least one special topic in
depth.
Work: In addition
to homework problems, students will study journal articles and present them to
the class.
Course Outline:
- The Twelvefold Way (Stanley I, Section 1.4): Binomial
coefficients, Stirling
numbers, etc.
- Recursions
and bijections: The two basic approaches to
enumeration. With examples.
- Other
approaches: Möbius function (incl.
inclusion-exclusion), Cancellation Principle (incl. reflection principle),
with applications to random walks.
- Generating
function and linear operator methods for solving recursions.
- Partitions
and Compositions