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PreprintCC BY 4.0arXiv

The weighted union-set conjecture is false

  • Yimeng Wang
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Abstract

We disprove a weighted generalization of the union-set conjecture [Fra95] raised in [Gow16]. We construct nonnegative weights on subsets of a finite ground set satisfying w(∅)=0 and w(A∪ B)≥min{w(A),w(B)}, while every coordinate belongs to an arbitrarily small fraction of the total weight.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026weighted,
  title = {{The weighted union-set conjecture is false}},
  author = {Yimeng Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25101},
  eprint = {2609.25101},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25101},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The weighted union-set conjecture is false
AU  - Yimeng Wang
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.25101
UR  - https://arxiv.org/abs/2609.25101
AB  - We disprove a weighted generalization of the union-set conjecture [Fra95] raised in [Gow16]. We construct nonnegative weights on subsets of a finite ground set satisfying w(∅)=0 and w(A∪ B)≥min{w(A),w(B)}, while every coordinate belongs to an arbitrarily small fraction of the total weight.
ER  -