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- W4366458384 abstract "Let $Asubseteq mathbb{Z}_{geq 0}$ be a finite set with minimum element $0$, maximum element $m$, and $ell$ elements in between. Write $(hA)^{(t)}$ for the set of integers that can be written in at least $t$ ways as a sum of $h$ elements of $A$. We prove that $(hA)^{(t)}$ is ``structured'' for [ h gtrsim frac{1}{e} mell t^{1/ell}, ] and prove a similar theorem for $Asubseteq mathbb{Z}^d$ and $h$ sufficiently large, with some explicit bounds on how large. Moreover, we construct a family of sets $A = A(m,ell,t)subseteq mathbb{Z}_{geq 0}$ for which $(hA)^{(t)}$ is not structured for $hll mell t^{1/ell}$." @default.
- W4366458384 created "2023-04-22" @default.
- W4366458384 creator A5070808697 @default.
- W4366458384 date "2023-04-17" @default.
- W4366458384 modified "2023-10-18" @default.
- W4366458384 title "On the structure of $t$-representable sumsets" @default.
- W4366458384 doi "https://doi.org/10.48550/arxiv.2304.08694" @default.
- W4366458384 hasPublicationYear "2023" @default.
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