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Keywords:
incidence structures; independent sets
incidence structures; independent sets
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 ${\mathcal J}^p=(G^p, M^p, \mathrel {{\mathrm I}^p})$ where $G^p$ ($M^p$) consists of all independent $p$-element subsets in $G$ ($M$) and $\mathrel {{\mathrm I}^p}$ is determined by some bijections. In the paper such incidence structures ${\mathcal J}$ are investigated the ${\mathcal J}^p$’s of which have their incidence graphs of the simple join form. Some concrete illustrations are included with small sets $G$ and $M$.
References:
[1] B. Ganter and R. Wille: Formale Begriffsanalyse. Mathematische Grundlagen. (Formal Concept Analysis Mathematical Foundations). Springer-Verlag, Berlin, 1996. (German) MR 1715047
[2] F. Buekenhout (ed.): Handbook of Incidence Geometry: Buldings and Foundations. Chap. 6. North-Holland, Amsterdam, 1995. MR 1360715
[3] F. Machala: Incidence structues of indpendent sets. Acta Univ. Palacki. Olomouc, Fac. rer. nat., Mathematica 38 (1999), 113–118. MR 1767196
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