English

Regular sets of lines in rank 3 polar spaces

Combinatorics 2024-06-17 v2

Abstract

There are 6 families of finite polar spaces of rank 33. The set of lines in a rank 33 polar space form a rank 55 association scheme. We determine the regular sets of minimal size in several of these polar spaces, and describe some examples. We also give a new family of Cameron--Liebler sets of generators in the polar spaces O+(10,q)O^+(10,q) when q=3hq = 3^h using a regular set of lines in O(7,q)O(7,q).

Keywords

Cite

@article{arxiv.2312.02397,
  title  = {Regular sets of lines in rank 3 polar spaces},
  author = {Ferdinand Ihringer and Morgan Rodgers},
  journal= {arXiv preprint arXiv:2312.02397},
  year   = {2024}
}