English

A family of hemisystems on the parabolic quadrics

Combinatorics 2019-08-26 v1

Abstract

We constuct a family of hemisystems of the parabolic quadric Q(2d,q)\mathcal{Q}(2d, q), for all ranks d2d \ge 2 and all odd prime powers qq, that admit Ω3(q)PSL2(q)\Omega_3(q) \cong \mathrm{PSL}_2(q). This yields the first known construction for d4d \ge 4.

Keywords

Cite

@article{arxiv.1908.08886,
  title  = {A family of hemisystems on the parabolic quadrics},
  author = {Jesse Lansdown and Alice C. Niemeyer},
  journal= {arXiv preprint arXiv:1908.08886},
  year   = {2019}
}