Name
Abstract | ||
|---|---|---|
In 1948, De Bruijn and Erdos proved that a finite linear space on @n points has at least @n 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. |
Year | DOI | Venue |
|---|---|---|
1983 | 10.1016/0012-365X(83)90071-7 | Discrete Mathematics |
Keywords | Field | DocType |
lower bound,projective plane,linear space | Real projective plane,Blocking set,Combinatorics,Complex projective space,Fano plane,Projective plane,Duality (projective geometry),Finite geometry,Mathematics,Projective space | Journal |
Volume | Issue | ISSN |
47, | 1 | Discrete Mathematics |
Citations | PageRank | References |
10 | 8.21 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| P Erdös | 1 | 626 | 190.85 |
| Ronald C. Mullin | 2 | 40 | 14.88 |
| V.T. Sós | 3 | 77 | 50.47 |
| D.R. Stinson | 4 | 150 | 32.16 |