Title: Lattice Paths Through ACSV
| Speaker: | Alex Kroitor |
| Affiliation: | University of Waterloo |
| Location: | MC 5479 |
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm.
Abstract: Analytic combinatorics in several variables uses complex analytic results to find coefficients in the series expansions of meromorphic functions. Typically this is used to find asymptotics of sequences by examining their associated generating functions. In the 2000's Bousquet-Melou (and others) used the kernel method, introduced in the late 60s and 70s, to find generating function expressions (in terms of certain multivariate rational functions) for certain kinds of walks in restricted regions. In particular Melczer and Mishna found asymptotics for these restricted walks when the step sets are symmetric in every axis. Further work by Melczer and Wilson found asymptotics under the weaker assumption that the step set is symmetric in all but one axis, except in the special case that the vector sum of all the steps is equal to zero. In the pre-seminar I will discuss the kernel method. In the main talk I will discuss how to solve the case where the vector sum is equal to zero. If time permits I will talk a little about the interesting combinatorial behaviour in this case and the treatment of the integrals that appear.