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N-cube

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In mathematics, an n-cube is a set of natural numbers that are sums of the form:

\sum_{i=1}^n c_i s_i \;\;\;\;\;\;\;\;\; (c_i\in \{0,1\})

for some finite set S=\{s_1,s_2,s_3,\dots,s_n\}.

In some sense, this mimics a geometric cube, which can be written C=\{(c_1,c_2,\dots,c_n)\} with ci as above. Indeed, an n-cube can be written as \{c_i\cdot S\ : 1\leq i\leq 2^n\} where C and S are as above and \cdot is the dot product. It is also a particular case of a generalized arithmetic progression.

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