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Register a new userStationary points at infinity for analytic combinatorics
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Added by
Stephen Melczer
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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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.
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