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Incidence structures of type \((p, n)\). (English) Zbl 1015.08001

Summary: Every incidence structure \({\mathcal J}\) (understood as a triple of sets \((G, M, I)\), \(I \subseteq G \times M\)) admits for every positive integer \(p\) an incidence structure \({\mathcal J}^p=(G^p, M^p, Ip)\) where \(G^p\) (\(M^p\)) consists of all independent \(p\)-element subsets in \(G\) (\(M\)) and \(Ip\) is determined by some bijections. In the paper incidence structures \({\mathcal J}\) are investigated whose \({\mathcal J}^p\)’s have incidence graphs of the simple join form. Some concrete illustrations are included with small sets \(G\) and \(M\).

MSC:

08A02 Relational systems, laws of composition
08A35 Automorphisms and endomorphisms of algebraic structures
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References:

[1] B. Ganter and R. Wille: Formale Begriffsanalyse. Mathematische Grundlagen. (Formal Concept Analysis Mathematical Foundations). Springer-Verlag, Berlin, 1996. · Zbl 0861.06001
[2] F. Buekenhout (ed.): Handbook of Incidence Geometry: Buldings and Foundations. Chap. 6. North-Holland, Amsterdam, 1995. · Zbl 0821.00012
[3] F. Machala: Incidence structues of indpendent sets. Acta Univ. Palacki. Olomouc, Fac. rer. nat., Mathematica 38 (1999), 113-118. · Zbl 0974.08001
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