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PreprintCC BY 4.0arXiv

New approaches to the Erdős Distinct Subset Sums Problem

Abstract

We present a new method of reproving the best known lower bound of the Erdős distinct subset sums problem. Although our lower bound is asymptotically the same as in Dubroff, Fox and Xu, it is slightly better for the case when n is odd. Besides, we also provide a new lower bound on the second largest element an−1.

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BibTeX
@misc{hasratyan2026approaches,
  title = {{New approaches to the Erdős Distinct Subset Sums Problem}},
  author = {Aren Hasratyan and Miklós Ruszinkó},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32580},
  eprint = {2610.32580},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32580},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - New approaches to the Erdős Distinct Subset Sums Problem
AU  - Aren Hasratyan
AU  - Miklós Ruszinkó
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32580
UR  - https://arxiv.org/abs/2610.32580
AB  - We present a new method of reproving the best known lower bound of the Erdős distinct subset sums problem. Although our lower bound is asymptotically the same as in Dubroff, Fox and Xu, it is slightly better for the case when n is odd. Besides, we also provide a new lower bound on the second largest element a_n−1.
ER  -