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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