Finite linear spaces and projective planes

P. Erdős, R. C. Mullin, V. T. Sós, D. R. Stinson

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

In 1948, De Bruijn and Erdös proved that a finite linear space on ν points has at least ν lines, with equality occurring if and only if the space is either a near-pencil (all points but one collinear) or a projective plane. In this paper, we study finite linear spaces which are not near-pencils. We obtain a lower bound for the number of lines (as a function of the number of points) for such linear spaces. A finite linear space which meets this bound can be obtained provided a suitable projective plane exists. We then investigate the converse: can a finite linear space meeting the bound be embedded in a projective plane.

Original languageEnglish
Pages (from-to)49-62
Number of pages14
JournalDiscrete Mathematics
Volume47
Issue numberC
DOIs
Publication statusPublished - 1983

Fingerprint

Projective plane
Linear Space
Line
Collinear
Converse
Equality
Lower bound
If and only if

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Finite linear spaces and projective planes. / Erdős, P.; Mullin, R. C.; Sós, V. T.; Stinson, D. R.

In: Discrete Mathematics, Vol. 47, No. C, 1983, p. 49-62.

Research output: Contribution to journalArticle

Erdős, P. ; Mullin, R. C. ; Sós, V. T. ; Stinson, D. R. / Finite linear spaces and projective planes. In: Discrete Mathematics. 1983 ; Vol. 47, No. C. pp. 49-62.
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