Extracting coefficients from generating functions: an application to lattice paths
Judy-anne Osborn (Department of Mathematics & Statistics, The University of Melbourne)
MSI Computational Mathematics (formerly AdvCom) Seminar SeriesDATE: 2006-10-09
TIME: 10:30:00 - 11:30:00
LOCATION: John Dedman Seminar Room G35
CONTACT: JavaScript must be enabled to display this email address.
ABSTRACT:
A new form of `Constant Term' method for extracting coefficients from rational generating functions is introduced. We have recently used this method to solve an open problem from the 1970's, that of enumerating directed lattice paths in a slit, subject to a pair of independent weights on each wall. This talk generalizes that problem and solution. The techniques utilized are a blend of combinatorial, analytic and algebraic. In particular we use the combinatorics of pavings to obtain closed form expressions for some orthogonal polynomials that occur in the generating functions.
