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In the context of submodular functions, I encountered the following statement :

For a vector $x \in \mathbb{R}^V$ and a subset $Y \subseteq V$ we define the expression $x(Y)$ as $\sum_{u \in Y}x(u)$.

$V$ is a set.

What does this statement mean ?

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    Oh, I get it now, silly me :)2011-06-08

2 Answers 2

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For sets $X$ and $Y$ the notation $X^Y$ means the following:

$ X^Y = \{f:Y \to X \mbox{ function}\} $

if $X$ is a field, then $X^Y$ can be given a structure of vector space over $X$ with the obvious point-wise operations.

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    @AnkurVijay: perhaps this old answer of mine is helpful: http://math.stackexchange.com/a/51062/26142012-02-02
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It refers to functions that go from Y to X.