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PreprintCC BY 4.0arXiv

Limitations of the slice rank method in additive combinatorics

  • Sankeerth Rao Karingula
  • Shachar Lovett
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Abstract

The slice rank method gives exponential bounds for sets with no three-term arithmetic progression in finite vector spaces of odd characteristic and for three-sunflower-free families of subsets of a fixed ground set. We show that for k≥4, every tensor that is nonzero exactly on the k-term arithmetic progression relation or the k-sunflower relation has maximal slice rank over every coefficient field. When the support is prescribed only on pairwise distinct inputs, we obtain comparable lower bounds, which likewise rule out exponential savings.

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Cite

BibTeXRIS
BibTeX
@misc{karingula2026limitations,
  title = {{Limitations of the slice rank method in additive combinatorics}},
  author = {Sankeerth Rao Karingula and Shachar Lovett},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27044},
  eprint = {2609.27044},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27044},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Limitations of the slice rank method in additive combinatorics
AU  - Sankeerth Rao Karingula
AU  - Shachar Lovett
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.27044
UR  - https://arxiv.org/abs/2609.27044
AB  - The slice rank method gives exponential bounds for sets with no three-term arithmetic progression in finite vector spaces of odd characteristic and for three-sunflower-free families of subsets of a fixed ground set. We show that for k≥4, every tensor that is nonzero exactly on the k-term arithmetic progression relation or the k-sunflower relation has maximal slice rank over every coefficient field. When the support is prescribed only on pairwise distinct inputs, we obtain comparable lower bounds, which likewise rule out exponential savings.
ER  -