“NP = P?” and restricted partitions

Abstract

This paper establishes a relationship between partition theory and the tractability of NP-complete problems. We define a special kind of partitions called restricted partitions and give a sufficient condition, in terms of some supposed property of restricted partitions, for “NP = P.” In validating the conclusion we propose a dynamic-programming algorithm with a set of natural numbers as its parameter, whose time complexity depends on the restricted partition property of this set.