Geodesic
Reconstructing a set from its subset sums: $2$-torsion-free groups
Discrete analysis (2024) Cet article a éte moissonné depuis la source Scholastica

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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.
Publié le : 
@article{DAS_2024_a7,
     author = {Federico Glaudo and Noah Kravitz},
     title = {Reconstructing a set from its subset sums: $2$-torsion-free groups},
     journal = {Discrete analysis},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2024_a7/}
}
TY  - JOUR
AU  - Federico Glaudo
AU  - Noah Kravitz
TI  - Reconstructing a set from its subset sums: $2$-torsion-free groups
JO  - Discrete analysis
PY  - 2024
UR  - http://geodesic.mathdoc.fr/item/DAS_2024_a7/
LA  - en
ID  - DAS_2024_a7
ER  - 
%0 Journal Article
%A Federico Glaudo
%A Noah Kravitz
%T Reconstructing a set from its subset sums: $2$-torsion-free groups
%J Discrete analysis
%D 2024
%U http://geodesic.mathdoc.fr/item/DAS_2024_a7/
%G en
%F DAS_2024_a7
Federico Glaudo; Noah Kravitz. Reconstructing a set from its subset sums: $2$-torsion-free groups. Discrete analysis (2024). http://geodesic.mathdoc.fr/item/DAS_2024_a7/