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Abstract: We consider a number of combinatorial problems in which rational generatingfunctions may be obtained, whose denominators have factors with certainsingularities. Specifically, there exist points near which one of the factorsis asymptotic to a nondegenerate quadratic. We compute the asymptotics of thecoefficients of such a generating function. The computation requires sometopological deformations as well as Fourier-Laplace transforms of generalizedfunctions. We apply the results of the theory to specific combinatorialproblems, such as Aztec diamond tilings, cube groves, and multi-setpermutations.



Author: Yuliy Baryshnikov, Robin Pemantle

Source: https://arxiv.org/







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