A glimpse at Analytic CombinatoricsAlgebra & Discrete Mathematics
|Hélène Barcelo, MSRI
|Mon, Dec 3 2012, 3:10PM
Analytic combinatorics is the quantitative study of combinatorial structures using methods from mathematical analysis, in particular complex and asymptotic analysis.
In their book, Analytic Combinatorics, P. Flajolet and R. Sedgewick describe a general approach in enumerative combinatorics that combines two types of methods: symbolic and analytic. The symbolic side is based on the automation of recursive constructions that yield characterizations of generating functions. The analytic side treats those functions as functions in the complex plane and leads first to asymptotic estimates of the number of objects, and then to precise characterizations of limit distributions.
Inspired by this book, we discuss how the continuous may help understand the discrete and quantify its properties.
Note the special time and room due to Colloquium at 4pm.