Sums, Products, and Dilates on Sparse Graphs
نویسندگان
چکیده
Let $A \subset \mathbb R$ and $G A \times A$. We prove that for any $\lambda \in R \setminus \{-1,0,1\}$, $ \max \{|A+_G A|, |A+_G \lambda |A\cdot_G A|\} \gg |G|^{6/11}.
منابع مشابه
Sums and Products along Sparse Graphs
In their seminal paper from 1983, Erdős and Szemerédi showed that any n distinct integers induce either n distinct sums of pairs or that many distinct products, and conjectured a lower bound of n2−o(1). They further proposed a generalization of this problem, in which the sums and products are taken along the edges of a given graph G on n labeled vertices. They conjectured a version of the sum-p...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2021
ISSN: ['1095-7146', '0895-4801']
DOI: https://doi.org/10.1137/20m1372184