It has been conjectured that in any matroid, if W1, W2, W3denote 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. © 1982.
Seymour, P. D. (1982). On the points-lines-planes conjecture. Journal of Combinatorial Theory, Series B, 33(1), 17–26. https://doi.org/10.1016/0095-8956(82)90054-5