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The Frobenius postage stamp problem, and beyond

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Abstract

Let A be a finite subset of \(\mathbb{Z}^n\), which generates \(\mathbb{Z}^n\) additively. We provide a precise description of the N-fold sumsets NA for N sufficiently large, with some explicit bounds on “sufficiently large.”

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Correspondence to A. Granville.

Additional information

Dedicated to Endre Szemerédi on the occasion of his 80th birthday

A.G. was funded by the European Research Council grant agreement No. 670239, and by the Natural Sciences and Engineering Research Council of Canada (NSERC) under the Canada Research Chairs program.

G.S. was supported by Ben Green’s Simons Investigator Grant 376201.

Many thanks to Vsevolod Lev and Tyrrell McAllister for pointing us to the references [11] and [13], respectively, Mel Nathanson for many insightful and useful remarks, and especially Bjorn Poonen for providing us with a layman’s guide to Presburger’s theorem in this context and Elliot Kaplan for useful explanations and pointing.

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Granville, A., Shakan, G. The Frobenius postage stamp problem, and beyond. Acta Math. Hungar. 161, 700–718 (2020). https://doi.org/10.1007/s10474-020-01073-y

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  • DOI: https://doi.org/10.1007/s10474-020-01073-y

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