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Your search keyword '"GRIGGS, T. S."' showing total 3 results
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3 results on '"GRIGGS, T. S."'

2. Existence results for pentagonal geometries

Author

Forbes, A. D., Griggs, T. S., and Stokes, K.

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.

Published
2022

3. FRAGMENTS IN SYMMETRIC CONFIGURATIONS WITH BLOCK SIZE 3.

Author

ERSKINE, G., GRIGGS, T. S., and ŠIRÁŇ, J.

Subjects
*TRIANGLES, *CONTENT analysis
Abstract

We begin the study of collections of three blocks which can occur in a symmetric configuration with block size 3, v3. Formulae are derived for the number of their occurrences and it is shown that the triangle, i.e. abf, ace, bcd, is a basis. It is also shown that symmetric con_gurations without triangles exist if and only if v = 15 or v ≥ 17. Such configurations containing "many" triangles are also discussed and a complete analysis of the triangle content of those with a cyclic automorphism is given. [ABSTRACT FROM AUTHOR]

Published
2022

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