Abstract
Let p be a prime and A, B be subsets of \(\mathbb{Z}/p{\mathbb{Z}}\). Freiman’s 2.4-theorem establishes that if \(|A|<\frac{1}{35}p\) and \(|A+A|<2.4|A|-3\), then A is contained in an arithmetic progression of length at most \(|A+A|-|A|+1\). When A and B are not very small and A+B is small, there are very few cases where something nontrivial about structure of A and B is known. In this paper we deal with this problem and we give a Freiman's 2.4-theorem-type result for different subsets. The main tool to do this is a Ruzsa triangle inequality-type result which is interesting in its own right.
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Huicochea, M. A Freiman’s 2.4 theorem-type result for different subsets. Acta Math. Hungar. 166, 393–406 (2022). https://doi.org/10.1007/s10474-022-01219-0
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DOI: https://doi.org/10.1007/s10474-022-01219-0