Existence results for pentagonal geometries

Forbes, A. D.; Griggs, T. S. and Stokes, K. (2022). Existence results for pentagonal geometries. Australasian Journal of Combinatorics, 82(1) pp. 95–114.

URL: https://ajc.maths.uq.edu.au/pdf/82/ajc_v82_p095.pd...

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.

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