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 \(M\).


08A02 Relational systems, laws of composition
08A35 Automorphisms and endomorphisms of algebraic structures
Full Text: DOI EuDML


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.