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Combinatorial optimization typically deals with optimizing over a finite set of objects that have some combinatorial structure (e.g. trees, matchings, matroids). Approximation algorithms, polyhedral methods, and integer programming are all on topic.

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Number of different combinations in a 0-1 knapsack problem with integer weights [closed]

My question is actually very similar to this other one: Given a vector of positive integers, count the number of combinations which have a sum that produces a different value. But, since this previous …