In this paper the number of directions determined by a set of q&n points of AG(2, q) is studied. To such a set we associate a curve of degree n and show that its linear components correspond to points that can be added to the set without changing the set of determined directions. The existence of li
On the number of k-subsets of a set of n points in the plane
β Scribed by Jacob E Goodman; Richard Pollack
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 175 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
It is shown that for fixed 1 ~ 0, if X C PG (d, q) contains (1 + ~)q~ points, then the number of r-fiats spanned by X is at least C(r.)q (r+l)ts+l-r), i.e. a positive fraction of the number of r-fiats in PG(s + 1,q).
## Abstract Halin's Theorem characterizes those infinite connected graphs that have an embedding in the plane with no accumulation points, by exhibiting the list of excluded subgraphs. We generalize this by obtaining a similar characterization of which infinite connected graphs have an embedding in
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