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arXiv · 2111.13766

Asymptotic equidistribution for partition statistics and topological invariants

Giulia Cesana·William Craig·Joshua Males
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Abstract

We provide a general framework for proving asymptotic equidistribution, convexity, and log concavity of coefficients of generating functions on arithmetic progressions. Our central tool is a variant of Wright's Circle Method proved by two of the authors with Bringmann and Ono, following work of Ngo and Rhoades. We offer a selection of different examples of such results, proving asymptotic equidistribution results for several partition statistics, modular sums of Betti numbers of two- and three-flag Hilbert schemes, and the number of cells of dimension a (mod b) of a certain scheme central in work of G\"ottsche.

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Giulia Cesana, William Craig, Joshua Males. 2021-11-26. Asymptotic equidistribution for partition statistics and topological invariants. https://arxiv.org/abs/2111.13766

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