Abstract
Erdos showed that every set of n positive integers contains a subset of size at least n/(k + 1) containing no solutions to x1 + . . . + xk = y. We prove that the constant 1/(k + 1) here is best possible by showing that if (Fm) is a multiplicative Følner sequence in N, then Fm has no k-sum-free subset of size greater than (1/(k + 1) + o(1))|Fm|.
| Original language | English |
|---|---|
| Pages (from-to) | 21-28 |
| Number of pages | 8 |
| Journal | Bulletin of the London Mathematical Society |
| Volume | 47 |
| Issue number | 1 |
| Early online date | 01 Dec 2014 |
| DOIs | |
| Publication status | Published - Feb 2015 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2014 London Mathematical Society.
ASJC Scopus subject areas
- General Mathematics