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Intersecting Matroids by a Hyperplane

✍ Scribed by Jiřı́ Tůma

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
267 KB
Volume
20
Category
Article
ISSN
0195-6698

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✦ Synopsis

Intersecting Matroids by a Hyperplane

We present an abstract matroid formulation of the geometric construction of intersecting the subspaces determined by a finite set of points of a projective space by a hyperplane containing a modular line spanned by two points of the set. It extends earlier results by Dilworth and the author.

📜 SIMILAR VOLUMES

Metric dimension of the intersections of
Metric dimension of the intersections of a point set with hyperplanes
✍ Tatsuo Goto 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 519 KB

In this paper we improve the construction of Goto (1993) to obtain the Main Theorem: Let n, m and k be arbitrary integers such that 0 < m < n -1 3 1 and m < k < min{2m, n -1). Then there exists a point set Xk,, in Euclidean n-space IR" such that (i) pdimX& = m and dimXk,, = k, (ii) pdim(X& n H) = m