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Article overview
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On the generalized restricted sumsets in abelian groups | Shanshan Du
; Hao Pan
; | Date: |
9 Sep 2016 | Abstract: | Suppose that $A$, $B$ and $S$ are non-empty subsets of a finite abelian group
$G$ with $|S|<p(G)$, where $p(G)$ is the least prime factor of $|G|$. Then the
generalized restricted sumset $$ Asplus{S}B:={a+b:,ain A, bin B,
a-b
otin S} $$ contains at least $$ min{|A|+|B|-3|S|,p(G)} $$ elements.
Further, we also have $$ |Asplus{S}B|geq min{|A|+|B|-|S|-2,p(G)}, $$
provided that both $|A|$ and $|B|$ are large with respect to $|S|$. | Source: | arXiv, 1609.2833 | Services: | Forum | Review | PDF | Favorites |
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