On the decomposition of sets of consecutive integers

Junhao Fan Shanghai High School

S.-T. Yau High School Science Awarded Papers mathscidoc:1702.35004

In this paper, we study the decomposition of sets of consecutive integers, i.e., how to express the set {0, 1, . . . ,mn−1} as the Minkovski sum of two sets, one with m terms and the other with n terms. First, we translate the problem into the language of polynomials. Then we use the properties of cyclotomic polynomials to determine the structure of all the solutions. Then, we deduce formulas for the number of such expressions. Finally, we give an algorithm to calculate the number of such expressions and analyze its computational complexity.
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  title={On the decomposition of sets of consecutive integers},
  author={Junhao Fan},
Junhao Fan. On the decomposition of sets of consecutive integers. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170227145344370088523.
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