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Extension of gravity centers configuration to Steiner triple systems. (English) Zbl 0867.05005

Summary: The centers of gravity of a simplex in a rational affine space and its subsimplices form a semilinear space. For this configuration several extensions to Steiner triple systems with the same point set are constructed by using totally symmetric loops.

MSC:

05B07 Triple systems
51E10 Steiner systems in finite geometry
Full Text: DOI

References:

[1] R. H. Bruck,A Survey of Binary Systems, Springer, Berlin/Göttingen/Heidelberg (1958). · Zbl 0081.01704
[2] G. Pickert, Konstruktion zweier (15,3,l)-Blockpläne,Abh. Math. Sem. Hamburg, Vol. 65 (1995) pp. 165-173. · Zbl 0859.51002 · doi:10.1007/BF02953323
[3] G. Pickert,Einführung in die endliche Geometrie, Stuttgart (1974).
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