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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

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Maximize sum of supermodular functions over nested sets

Let $R$ be a function that maps a set and a positive integer to a real positive number. We have that for any positive integer $t$ and $S \subseteq \{1, \ldots, t\}$, $R(S, t)$ satisfies: For all $t …