Syllabus for Math 192r (Algebraic Combinatorics)

The following mathematical topics will be covered:

* Binomial coefficients and Pascal's triangle

* Calculus of finite differences

* Stirling numbers and Bell numbers

* Fibonacci numbers and linear recurrences

* Rational and algebraic generating functions, with applications to probability

* Continued fractions and continuants

* Catalan objects and lattice animals

* Transfer matrices

* Partitions and compositions

* Combinatorial reciprocity theorems

* q-enumeration and tiling

* Determinants and condensation, number walls, and frieze patterns

* Signed enumeration and applications (the theorems of Vandermonde, Cayley-Hamilton, and Gessel-Viennot)

Maintained by Jim Propp.

Last updated September 3, 2001.