Shape of the asymptotic maximum sum-free sets in integer lattice grids
| Autor: | Liu, Hong, Wang, Guanghui, Wilkes, Laurence, Yang, Donglei |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We determine the shape of all sum-free sets in $\{1,2,\ldots,n\}^2$ of size close to the maximum $\frac{3}{5}n^2$, solving a problem of Elsholtz and Rackham. We show that all such asymptotic maximum sum-free sets lie completely in the stripe $\frac{4}{5}n-o(n)\le x+y\le\frac{8}{5}n+ o(n)$. We also determine for any positive integer $p$ the maximum size of a subset $A\subseteq \{1,2,\ldots,n\}^2$ which forbids the triple $(x,y,z)$ satisfying $px+py=z$. Comment: 18 pages, 8 figures |
| Databáze: | arXiv |
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