Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 149, Issue 10, Pages 4073-4082Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/proc/15608
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Funding
- European Research Council [670239]
- Natural Sciences and Engineering Research Council of Canada (NSERC) under the Canada Research Chairs program
- European Research Council (ERC) [670239] Funding Source: European Research Council (ERC)
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The research proves that the set NA has a certain easily-described structure when N >= b - l, as recently conjectured. It also classifies sets A for which this bound cannot be improved.
Let A = {0 = a(0) < a(1) < center dot center dot center dot < a(l+1) = b} be a finite set of non-negative integers. We prove that the sumset NA has a certain easily-described structure, provided that N >= b - l, as recently conjectured (see A. Granville and G. Shakan [Acta Math. Hungar. 161 (2020), pp. 700-718]). We also classify those sets A for which this bound cannot be improved.
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