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Existence results for pentagonal geometries

07/17/2020

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by Anthony D. Forbes, et al.

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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.

Anthony D. Forbes
1 publication
Terry S. Griggs
1 publication
Klara Stokes
2 publications

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