A lower bound for the size of a Minkowski sum of dilates. (English) Zbl 1231.11013
An \(n\)-component of a finite set of integers is the intersection with a congruence class modulo \(n\). Let \(k\) be an odd prime, \(A\) a finite set of integers with \(0\in A\), \(\gcd(A)=1\) and \(|A|>8k^k\). The authors prove that if \(A\) has a \(k\)-component involving at most \(k-1\) distinct \(k^2\)-components, then
\[
|2\cdot A+k\cdot A|>(k+2)|A|.
\]
Reviewer: Florin Nicolae (Berlin)
References:
| [1] | DOI: 10.1017/S0963548309990307 · Zbl 1200.11007 · doi:10.1017/S0963548309990307 |
| [2] | DOI: 10.1017/S096354830800919X · Zbl 1191.11007 · doi:10.1017/S096354830800919X |
| [3] | DOI: 10.4064/aa131-1-4 · Zbl 1165.11031 · doi:10.4064/aa131-1-4 |
| [4] | Cilleruelo, J. Combin. Number Theory 2 (2010) |
| [5] | DOI: 10.1007/BF02771981 · Zbl 1127.52021 · doi:10.1007/BF02771981 |
| [6] | DOI: 10.1090/S0002-9939-08-09385-4 · Zbl 1220.11013 · doi:10.1090/S0002-9939-08-09385-4 |
| [7] | DOI: 10.4064/aa129-4-5 · Zbl 1156.11011 · doi:10.4064/aa129-4-5 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
