Fragments in symmetric configurations with block size 3

2021/08/15 by Grahame Erskine, Erskine, Grahame, Terry S. Griggs +4
Engineering · Materials Science · Mathematics · #05B30 #Advanced Materials and Mechanics #Combinatorics (math.CO) #FOS: Mathematics #Quasicrystal Structures and Properties #graph theory and CDMA systems #math.CO #msc:05B30

paper · pdf · doi:10.48550/arxiv.2108.06795

9 pages, 4 figures

arxiv created 2021/08/15 · openalex publication_date 2021/08/15 · arxiv updated 2021/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 occurrences of these 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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