Patterns without a popular difference
Which finite sets $P \subseteq \mathbb{Z}^r$ with $|P| \ge 3$ have the following property: for every $A \subseteq [N]^r$, there is some nonzero integer $d$ such that $A$ contains $(\alpha^{|P|} - o(1))N^r$ translates of $d \cdot P = \{d p : p \in P\}$, where $\alpha = |A|/N^r$? Green showed th...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Alliance of Diamond Open Access Journals
2022
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| Online Access: | https://hdl.handle.net/1721.1/145889 |