Title: Multivariate Limit Theorems and Algebraic Generating Functions
| Speaker |
Tia Ruza |
| Affiliation | University of À¶Ý®ÊÓƵ |
| Location | MC 5479 |
Abstract: The field of analytic combinatorics in several variables
(ACSV) is dedicated to the creation of effective techniques to study the large-scale behaviour of combinatorial objects. This talk provides results for two areas of ACSV: limit theorems and asymptotics of algebraic generating functions. First, I will describe an automated approach to proving local central limit theorems and its applications to a variety of examples. Included in these examples will be a family of permutations with restricted cycles, integer compositions with tracked summands and n-colour compositions with tracked summands. The second half of the talk will survey techniques for analyzing multivariate algebraic generating functions, going into detail specifically for the process of embedding an algebraic generating function into a sub-series of a rational function of more variables. For both parts of the talk, SageMath code which automates the methods discussed will be demonstrated for various examples.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.