On restricted sums (Q2711616)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On restricted sums |
scientific article |
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11 September 2001
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sumsets
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finite Abelian groups
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subgroups
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unions of cosets
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0.8992305
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0.8928447
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0.8913807
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On restricted sums (English)
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Let \(A\) be a finite set in a commutative group, \(|A|=n\). It is proved that for \(n\geq 33\), the number of elements representable in the form \(a+a'\), with \(a,a'\in A\) and \(a\neq a'\), is at least \(3n/2\) except when \(A\) is contained in a subgroup of \(<3n/2\) elements. Equality occurs when \(A\) is the union of two cosets of a subgroup. This complements a result of Dias da Silva and Hamidoune, which asserts that in case of a cyclic group of prime order the corresponding cardinality is at least \(2n-3\).
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