English

Intersection numbers for subspace designs

Combinatorics 2015-10-16 v1

Abstract

Intersection numbers for subspace designs are introduced and qq-analogs of the Mendelsohn and K\"ohler equations are given. As an application, we are able to determine the intersection structure of a putative qq-analog of the Fano plane for any prime power qq. It is shown that its existence implies the existence of a 22-(7,3,q4)q(7,3,q^4)_q subspace design. Furthermore, several simplified or alternative proofs concerning intersection numbers of ordinary block designs are discussed.

Keywords

Cite

@article{arxiv.1405.6110,
  title  = {Intersection numbers for subspace designs},
  author = {Michael Kiermaier and Mario Osvin Pavčević},
  journal= {arXiv preprint arXiv:1405.6110},
  year   = {2015}
}
R2 v1 2026-06-22T04:22:05.521Z