Syllabus for Math 491 (Algebraic Combinatorics)

The following mathematical topics will be covered:

* Binomial coefficients and Pascal's triangle

* Calculus of finite differences

* Fibonacci numbers and linear recurrences

* Rational and algebraic generating functions

* Continued fractions and continuants

* Catalan objects and lattice animals

* Transfer matrices

* Combinatorial reciprocity theorems

* q-enumeration and tiling

* Determinants and condensation, number walls, triangulations, and frieze patterns

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

* Markoff numbers

* Somos sequences

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Last updated April 22, 2003.