Analytic combinatorics

  • Date:
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Stephan Wagner from Stellenbosch University
  • Contact person: Cecilia Holmgren
  • Seminarium

This is the first of a series of lectures in analytic combinatorics. Fika will be served at 10.00.

Abstract:

The analysis of generating functions is a powerful tool for the exact and asymptotic enumeration of discrete structures as well as the study of parameters of random structures. Typical examples include trees and other types of graphs, words over finite alphabets, permutations, compositions, number partitions and set partitions. Within the framework of analytic combinatorics, one applies tools from real and complex analysis to the study of such structures.

This course provides an introduction to some common techniques in this area, such as singularity analysis of generating functions, the saddle point method and the quasi-power theorem. By means of different topical examples, I will show how these methods can be applied to determine asymptotic enumeration formulas as well as limit theorems for random discrete structures.