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Structural Approach to Subset Sum Problems

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Abstract

We discuss results obtained jointly with Van Vu on the length of arithmetic progressions in \(\ell \)-fold sumsets of the form

$$\begin{aligned} \ell \mathcal {A}=\{a_1+\dots +a_\ell ~|~a_i\in \mathcal {A}\} \end{aligned}$$

and

$$\begin{aligned} \ell \mathcal {A}=\{a_1+\dots +a_\ell ~|~a_i\in \mathcal {A}\text { all distinct}\}, \end{aligned}$$

where \(\mathcal {A}\) is a set of integers. Applications are also discussed.

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Acknowledgments

The author would like to express his gratitude to one of the referees whose contributions to the presentation of the material are greatly appreciated.

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Correspondence to Endre Szemerédi.

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Supported by OTKA NK 104183 and by ERC-AdG 321104.

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Szemerédi, E. Structural Approach to Subset Sum Problems. Found Comput Math 16, 1737–1749 (2016). https://doi.org/10.1007/s10208-016-9326-8

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