Fragments in symmetric configurations with block size 3

Erskine, Grahame; Griggs, Terry and Širáň, Jozef (2022). Fragments in symmetric configurations with block size 3. Acta Mathematica Universitatis Comenianae, 91(2) pp. 101–111.

URL: http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/am...

Abstract

We begin the study of collections of three blocks which can occur in a symmetric configuration with block size 3, v_3. 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 configurations 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.

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