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PreprintCC BY 4.0HAL

The Davenport constant of low-dimensional boxes

  • Benjamin Girard
  • Alain Plagne
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Abstract

In this paper, we study the maximal length of a minimal zero-sum sequence over [ [ −m,m ] ]d having a support of size d+1. When d=2, we find the exact value of this maximal length for all m ≥ 2, as well as the exact structure of all extremal sequences for this problem. When d=3, we obtain lower and upper bounds that asymptotically match each other as m tends to infinity. This allows us to improve on the best known lower bounds for the Davenport constant of low-dimensional boxes.

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Cite

BibTeXRIS
BibTeX
@misc{girard2026davenport,
  title = {{The Davenport constant of low-dimensional boxes}},
  author = {Benjamin Girard and Alain Plagne},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16562},
  eprint = {2610.16562},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05794482v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Davenport constant of low-dimensional boxes
AU  - Benjamin Girard
AU  - Alain Plagne
PY  - 2026
DA  - 2026/10/12
PB  - HAL
DO  - 10.48550/arxiv.2610.16562
UR  - https://hal.science/hal-05794482v1
AB  - In this paper, we study the maximal length of a minimal zero-sum sequence over [ [ −m,m ] ]^d having a support of size d+1. When d=2, we find the exact value of this maximal length for all m ≥ 2, as well as the exact structure of all extremal sequences for this problem. When d=3, we obtain lower and upper bounds that asymptotically match each other as m tends to infinity. This allows us to improve on the best known lower bounds for the Davenport constant of low-dimensional boxes.
ER  -