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A given subset A of natural numbers is said to be complete if every element of N is the sum of distinct terms taken from A. This topic is strongly connected to the knapsack problem which is known to be NP complete. Interestingly if A and B are complete sequences then \(A\times B\) is not necessarily complete in \(\mathbb {N}^2\) . In this paper we consider a modular version of this problem, motivated by the communication complexity problem of [2].

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On the Distribution of Subset Sums of Certain Sets in \(\mathbb {Z}^2_p\) and in \(\mathbb {N}^2\)

  • 会议论文

  • 发表日期：

    2025年

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  • Norbert Hegyvári

摘要

A given subset A of natural numbers is said to be complete if every element of N is the sum of distinct terms taken from A. This topic is strongly connected to the knapsack problem which is known to be NP complete. Interestingly if A and B are complete sequences then \(A\times B\) is not necessarily complete in \(\mathbb {N}^2\) . In this paper we consider a modular version of this problem, motivated by the communication complexity problem of [2].