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.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics