Stationary points at infinity for analytic combinatorics
Combinatorics
2021-02-22 v3 Symbolic Computation
Algebraic Geometry
Abstract
On complex algebraic varieties, height functions arising in combinatorial applications fail to be proper. This complicates the description and computation via Morse theory of key topological invariants. Here we establish checkable conditions under which the behavior at infinity may be ignored, and the usual theorems of classical and stratified Morse theory may be applied. This allows for simplified arguments in the field of analytic combinatorics in several variables, and forms the basis for new methods applying to problems beyond the reach of previous techniques.
Cite
@article{arxiv.1905.05250,
title = {Stationary points at infinity for analytic combinatorics},
author = {Yuliy Baryshnikov and Stephen Melczer and Robin Pemantle},
journal= {arXiv preprint arXiv:1905.05250},
year = {2021}
}
Comments
Updated and simplified presentation and statements of main results