Stationary Points at Infinity for Analytic Combinatorics

Yuliy Baryshnikov, Stephen Melczer, Robin Pemantle

Research output: Contribution to journalArticlepeer-review


On complex algebraic varieties, height functions arising in combinatorial applications fail to be proper. This complicates both 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.

Original languageEnglish (US)
Pages (from-to)1631-1664
Number of pages34
JournalFoundations of Computational Mathematics
Issue number5
StatePublished - Oct 2022


  • ACSV
  • Analytic combinatorics
  • Computer algebra
  • Critical point
  • Intersection cycle
  • Stratified Morse theory

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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