Improvement of inequalities for the $(r,q)$-structures and some geometrical connections

Vojtech Bálint; Philippe Lauron

Displaying similar documents to “Improvement of inequalities for the $(r, q)$ -structures and some geometrical connections”

On stabbing triangles by lines in 3-space

Boris Aronov, Jiří Matoušek (1995)

Commentationes Mathematicae Universitatis Carolinae

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We give an example of a set $P$ of $3 n$ points in $ℝ 3$ such that, for any partition of $P$ into triples, there exists a line stabbing $Ω (\sqrt{n})$ of the triangles determined by the triples.

Incidence structures of type $(p, n)$

František Machala (2003)

Czechoslovak Mathematical Journal

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

On Mazurkiewicz sets

Marta N. Charatonik, Włodzimierz J. Charatonik (2000)

Commentationes Mathematicae Universitatis Carolinae

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A Mazurkiewicz set $M$ is a subset of a plane with the property that each straight line intersects $M$ in exactly two points. We modify the original construction to obtain a Mazurkiewicz set which does not contain vertices of an equilateral triangle or a square. This answers some questions by L.D. Loveland and S.M. Loveland. We also use similar methods to construct a bounded noncompact, nonconnected generalized Mazurkiewicz set.

Displaying similar documents to “Improvement of inequalities for the ( r , q ) -structures and some geometrical connections”

On stabbing triangles by lines in 3-space

Incidence structures of type ( p , n )

On Mazurkiewicz sets

Displaying similar documents to “Improvement of inequalities for the $(r, q)$ -structures and some geometrical connections”

Incidence structures of type $(p, n)$