Critical points at infinity for analytic combinatorics

Yuliy Baryshnikov, Stephen Melczer, Robin Pemantle

Published 2019-05-13Version 1

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.