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- W4377148557 abstract "For a finite multiset $A$ of an abelian group $G$, let $text{FS}(A)$ denote the multiset of the $2^{|A|}$ subset sums of $A$. It is natural to ask to what extent $A$ can be reconstructed from $text{FS}(A)$. We fully solve this problem for $2$-torsion-free groups $G$ by giving characterizations, both algebraic and combinatorial, of the fibers of $text{FS}$. Equivalently, we characterize all pairs of multisets $A,B$ with $text{FS}(A)=text{FS}(B)$. Our results build on recent work of Ciprietti and the first author." @default.
- W4377148557 created "2023-05-21" @default.
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- W4377148557 date "2023-05-18" @default.
- W4377148557 modified "2023-09-29" @default.
- W4377148557 title "Reconstructing a set from its subset sums: $2$-torsion-free groups" @default.
- W4377148557 doi "https://doi.org/10.48550/arxiv.2305.11062" @default.
- W4377148557 hasPublicationYear "2023" @default.
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