Multivariate Analytic Combinatorics: Functions with Algebraic Singularities

Series: 
Combinatorics Seminar
Friday, October 9, 2015 - 15:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Georgia Tech
,  
Organizer: 
Flajolet and Odlyzko (1990) derived asymptotic formulae for the coefficients of a class of univariate generating functions with algebraic singularities. These results have been extended to classes of multivariate generating functions by Gao and Richmond (1992) and Hwang (1996, 1998), in both cases by reducing the multivariate case to the univariate case. Pemantle and Wilson (2013) outlined new multivariate analytic techniques and used them to analyze the coefficients of rational generating functions. In this talk, we discuss these multivariate analytic techniques and use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities.  We will also look at how to apply such formulae to practical problems.