S.-T. Yau High School Science Awarded Papersmathscidoc:1702.35004
2016
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.
@inproceedings{junhao2016on,
title={On the decomposition of sets of consecutive integers},
author={Junhao Fan},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170227145344370088523},
year={2016},
}
Junhao Fan. On the decomposition of sets of consecutive integers. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170227145344370088523.