2008/10/27 by Yuliy Baryshnikov, Baryshnikov, Yuliy, Robin Pemantle +1
Computer Science · Mathematics · #05A16 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.0810.4898
openalex publication_date 2008/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.