Stationary points at infinity for analytic combinatorics

Autor:	Baryshnikov, Yuliy, Melczer, Stephen, Pemantle, Robin
Rok vydání:	2019
Předmět:	Mathematics - Combinatorics Computer Science - Symbolic Computation Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	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. Comment: Updated and simplified presentation and statements of main results
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1905.05250 Zobrazit plný text záznamu View this record from Arxiv