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Representing Submodular Functions As Maxima of Additive Functions

According to this paper, "every submodular function can be represented as a maximum of additive valuations." It gives an algebraic description as well, but I am having trouble internalizing ...
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Seemingly conflicting notions of a function

Throughout my mathematical education, I have seen a few, seemingly, different and conflicting notions of what a function is: A function is a a type of mathematical object that maps every element of a ...
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