Embedding linear spaces with two line degrees in finite projective planes. (English) Zbl 0586.51005
A linear space is an incidence structure with points, at least two lines, and incidence, such that any two distinct points are incident with just one line, and any line is incident with at least two points. The number of points on a line is called the line degree. The author studies those finite linear spaces which contain only lines of two degrees, n and n-k, and whose number of lines is at most \(n^ 2+n+1.\) He succeeds in classifying all these linear spaces and investigates their embeddability in finite projective planes. The result is that, if n is large compared with k, then any such linear space can be embedded in a projective plane of order n-1 or n.
Reviewer: R.Artzy
MSC:
| 51A45 | Incidence structures embeddable into projective geometries |
| 51E15 | Finite affine and projective planes (geometric aspects) |
| 51E30 | Other finite incidence structures (geometric aspects) |
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