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additive basis (Definition)

A subset $ A$ of $ \mathbb{Z}$ is an (additive) basis of order $ n$ if

$\displaystyle nA=\mathbb{N}\cup\{0\},$    

where $ nA$ is $ n$-fold sumset of $ A$. Usually it is assumed that 0 belongs to $ A$ when saying that $ A$ is an additive basis.



"additive basis" is owned by bbukh.
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See Also: asymptotic basis, Schnirelmann density, essential component

Other names:  basis
Also defines:  order of additive basis
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Cross-references: sumset, subset
There are 47 references to this entry.

This is version 3 of additive basis, born on 2002-12-26, modified 2002-12-26.
Object id is 3831, canonical name is Basis2.
Accessed 9228 times total.

Classification:
AMS MSC: 11B13 (Number theory :: Sequences and sets :: Additive bases)
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