Partition Problems and a Pattern of Vertical Sums

Authors

  • Eunice Krinsky California State University, Dominguez Hills
  • Serban Raianu California State University, Dominguez Hills
  • Alexander Wittmond California State University, Dominguez Hills

DOI:

https://doi.org/10.46787/pump.v1i0.149

Keywords:

congruence modulo an integer; partitions of sets; partitions of integers

Abstract

We give a possible explanation for the mystery of a missing number in the statement of a problem that asks for the non-negative integers to be partitioned into three subsets. Based on a pattern of sums of certain elements in the three sets, we find a more standard solution to the problem, using only congruence modulo five. We also show that the original statement plays a special role among all statements that satisfy the same pattern of the sums.

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Published

2018-01-05

How to Cite

Krinsky, E., Raianu, S., & Wittmond, A. (2018). Partition Problems and a Pattern of Vertical Sums. The PUMP Journal of Undergraduate Research, 1, 30–47. https://doi.org/10.46787/pump.v1i0.149

Issue

Vol. 1 (2018): PUMP Journal of Undergraduate Research

Section

Articles

License

The author(s) will retain the copyright, but by submitting the article agree to grant permission to the PUMP Journal of Undergraduate Research to publish, distribute, and archive the article. The author(s) will acknowledge prior publication in the PUMP Journal of Undergraduate Research for all future uses of the article or parts of it.