CO 630Algebraic Enumeration

The algebra of formal Laurent series. Multivariate ordinary generating functions and exponential generating functions. The Lagrange Implicit Function Theorem, the MacMahon Master Theorem. Enumeration of planar triangulations. The Transfer Matrix method. Sieve methods, Inclusion/Exclusion, Möbius inversion. Pólya Enumeration, Enumeration of Trees. Basic hypergeometric series, q-analogues, Rogers-Ramanujan identities. Asymptotic methods.