Geodesic
Fragments in symmetric configurations with block size 3
Grahame Erskine1 ; Terry Griggs1 ; Jozef Širáň2 ; Grahame Erskine ; Terry Griggs ; Jozef Širáň
1Open University, Milton Keynes, UK
2Open University, Milton Keynes, UK; Slovak University of Technology, Bratislava, Slovakia
Acta mathematica Universitatis Comenianae, Tome 91 (2022) no. 2, pp. 101-111 
Grahame Erskine; Terry Griggs; Jozef Širáň; Grahame Erskine; Terry Griggs; Jozef Širáň. Fragments in symmetric configurations with block size 3. Acta mathematica Universitatis Comenianae, Tome 91 (2022) no. 2, pp. 101-111. http://geodesic.mathdoc.fr/item/AMUC_2022_91_2_a0/
@article{AMUC_2022_91_2_a0,
     author = {Grahame Erskine and Terry Griggs and Jozef \v{S}ir\'a\v{n} and Grahame Erskine and Terry Griggs and Jozef \v{S}ir\'a\v{n}},
     title = { Fragments in symmetric configurations with block size 3},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {101--111},
     year = {2022},
     volume = {91},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2022_91_2_a0/}
}
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Voir la notice de l'article provenant de la source Comenius University

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 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.