Existence results for pentagonal geometries
Combinatorics
2020-07-22 v1 Discrete Mathematics
Abstract
New results on pentagonal geometries PENT(k,r) with block sizes k = 3 or k = 4 are given. In particular we completely determine the existence spectra for PENT(3,r) systems with the maximum number of opposite line pairs as well as those without any opposite line pairs. A wide-ranging result about PENT(3,r) with any number of opposite line pairs is proved. We also determine the existence spectrum of PENT(4,r) systems with eleven possible exceptions.
Cite
@article{arxiv.2007.10810,
title = {Existence results for pentagonal geometries},
author = {Anthony D. Forbes and Terry S. Griggs and Klara Stokes},
journal= {arXiv preprint arXiv:2007.10810},
year = {2020}
}