PlanetMath: sumset

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sumset

(Definition)

Let $A_1, A_2, \dotsc, A_n$ be subsets of an additive group . The sumset

$\displaystyle A_1+A_2+\dotsb+A_n$

is the set of all elements of the form $a_1+a_2+\dotsb+a_n$ , where $a_i \in A_i$ .

In geometry a sumset is often called Minkowski sum.

"sumset" is owned by bbukh.

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Other names:

Minkowski sum

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Cross-references: geometry, additive group, subsets
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This is version 2 of sumset, born on 2002-12-26, modified 2003-09-26.
Object id is 3830, canonical name is Sumset.
Accessed 3617 times total.

Classification:

AMS MSC:	11B13 (Number theory :: Sequences and sets :: Additive bases)
	11B05 (Number theory :: Sequences and sets :: Density, gaps, topology)

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