The structure of higher sumsets
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- by Vsevolod F. Lev PDF
- Proc. Amer. Math. Soc. 150 (2022), 5165-5177 Request permission
Abstract:
Merging together a result of Nathanson from the early 70s and a recent result of Granville and Walker, we show that for any finite set $A$ of integers with $\min (A)=0$ and $\gcd (A)=1$ there exist two sets, the “head” and the “tail”, such that if $m\ge \max (A)-|A|+2$, then the $m$-fold sumset $mA$ consists of the union of the head, the appropriately shifted tail, and a long block of consecutive integers separating them. We give sharp estimates for the length of the block, and find all those sets $A$ for which the bound $\max (A)-|A|+2$ cannot be substantially improved.References
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Additional Information
- Vsevolod F. Lev
- Affiliation: Department of Mathematics, The University of Haifa at Oranim, Tivon 36006, Israel
- Email: seva@math.haifa.ac.il
- Received by editor(s): October 8, 2021
- Received by editor(s) in revised form: February 26, 2022
- Published electronically: August 19, 2022
- Communicated by: Isabella Novik
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 5165-5177
- MSC (2020): Primary 11B13; Secondary 11D07, 11A99
- DOI: https://doi.org/10.1090/proc/16128