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- W1822981364 abstract "For a finite abelian group $G$ and positive integers $m$ and $h$, we let $$rho(G, m, h) = min {|hA| ; : ; A subseteq G, |A|=m}$$ and $$rho_{pm} (G, m, h) = min {|h_{pm} A| ; : ; A subseteq G, |A|=m},$$ where $hA$ and $h_{pm} A$ denote the $h$-fold sumset and the $h$-fold signed sumset of $A$, respectively. The study of $rho(G, m, h)$ has a 200-year-old history and is now known for all $G$, $m$, and $h$. In previous work we provided an upper bound for $rho_{pm} (G, m, h)$ that we believe is exact, and proved that $rho_{pm} (G, m, h)$ agrees with $rho (G, m, h)$ when $G$ is cyclic. Here we study $rho_{pm} (G, m, h)$ for elementary abelian groups $G$; in particular, we determine all values of $m$ for which $rho_{pm} (mathbb{Z}_p^2, m, 2)$ equals $rho (mathbb{Z}_p^2, m, 2)$ for a given prime $p$." @default.
- W1822981364 created "2016-06-24" @default.
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- W1822981364 date "2014-12-04" @default.
- W1822981364 modified "2023-09-27" @default.
- W1822981364 title "On the Minimum Size of Signed Sumsets in Elementary Abelian Groups" @default.
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