The small Davenport constant of E₂× C₃^r for 0≤ r≤3

@misc{volkmann2026small,
  title = {{The small Davenport constant of $E_2\times C_3^r$ for $0\le r\le3$}},
  author = {Andreas Volkmann},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37262},
  eprint = {2609.37262},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37262},
}

TY  - UNPB
TI  - The small Davenport constant of E_2× C_3^r for 0≤ r≤3
AU  - Andreas Volkmann
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37262
UR  - https://arxiv.org/abs/2609.37262
AB  - Let E_2 be the extraspecial group of order 3^5 and exponent three. We prove that d(E_2× C_3^r)=2r+10 for 0≤ r≤3. The upper bounds follow from signed zero-block identities and two finite statements in the four-dimensional symplectic space over 𝔽_3. The first supplies edge weights for all completable balanced triangles on any indexed list of at most sixteen nonzero vectors. The second supplies weights for the direction families that can occur in a critical list with no central terms. We give complete coverage arguments, exact certificate files, and separately implemented checking programs. A compression argument removes any need for an induction through smaller list lengths in the sixteen-term potential theorem. The formula for r≥4 remains open.
ER  -