Abstract
Let ∪, △, ⨄ and + denote set-union, symmetric set-difference, multiset-union and real number addition, respectively. We consider low complexity inverse mappings (algorithms which return the subset of a given sum) defined on sum-distinct elements from (2 S , ∪), (2 S , △), (2 S , ⨄) and (S n , +) where 2 S is a power set of an n-element set S and S n ≜ {0, 1,…, 2 n − 1}. Within each of the above pair, mappings are related to generating functions of the respective sum-distinct sets. Between compatible pairs, they are related by a subset-sum property, e.g. if L ∈ 2 S is sum-distinct in (2 S , ∪), then L is sum-distinct in (2 S , △).
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