Asymptotics of multivariate sequences, part III: Quadratic points

Yuliy Baryshnikov, Robin Pemantle

Research output: Contribution to journalArticlepeer-review


We consider a number of combinatorial problems in which rational generating functions may be obtained, whose denominators have factors with certain singularities. Specifically, there exist points near which one of the factors is asymptotic to a nondegenerate quadratic. We compute the asymptotics of the coefficients of such a generating function. The computation requires some topological deformations as well as Fourier-Laplace transforms of generalized functions. We apply the results of the theory to specific combinatorial problems, such as Aztec diamond tilings, cube groves, and multi-set permutations.

Original languageEnglish (US)
Pages (from-to)3127-3206
Number of pages80
JournalAdvances in Mathematics
Issue number6
StatePublished - Dec 20 2011
Externally publishedYes


  • Amoeba
  • Aztec diamond
  • Cube grove
  • Fourier transform
  • Fourier-Laplace
  • Generalized function
  • Hyperbolic polynomial
  • Lacuna
  • Multivariate generating function
  • Quantum random walk
  • Random tiling

ASJC Scopus subject areas

  • General Mathematics


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