1 research outputs found
Stationary points at infinity for analytic combinatorics
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 result