A theorem on the average number of subfaces in arrangements and oriented matroids

Komei Fukuda, Akihisa Tamura, Takeshi Tokuyama

Research output: Contribution to journalArticle

3 Citations (Scopus)


It is known that for simple arrangements in the d-dimensional Euclidean space RdThe average number of j-dimensional subfaces of a k-dimensional face is less than {Mathematical expression}. In this paper, we show that this is also true for all arrangements in Rd and for all oriented matroids, and we give combinatorial proofs.

Original languageEnglish
Pages (from-to)129-142
Number of pages14
JournalGeometriae Dedicata
Issue number2
Publication statusPublished - 1993 Aug 1
Externally publishedYes


ASJC Scopus subject areas

  • Geometry and Topology

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