On the points-lines-planes conjecture

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10 Scopus citations


It has been conjectured that in any matroid, if W1, W2, W3 denote the number of points, lines, and planes respectively, then W22 ≥ W1W3. We prove this conjecture (and some strengthenings) for matroids in which no line has five or more points, thus generalizing a result of Stonesifer, who proved it for graphic matroids.

Original languageEnglish (US)
Pages (from-to)17-26
Number of pages10
JournalJournal of Combinatorial Theory, Series B
Issue number1
StatePublished - Aug 1982
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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