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Galois geometry, finite projective and affine spaces, polar spaces, partial geometries, generalized polygons, near polygons, and other finite incidence geometries.

3 votes
Accepted

An upper bound on the number of sets of parallel lines covering points in a finite plane?

If a set $S$ is evenly covered by lines in $n$ slopes, then $n \le |S|-1$ because through every point $p$, there are at most $|S|-1$ lines connecting $p$ to other points in the set, and any other slop …
Douglas Zare's user avatar
7 votes

Blocking sets in three dimensional finite affine spaces

Here is a slightly better lower bound. If there are fewer than $2q^2$ points then there is some line that hits the set at most once. Consider the $q+1$ planes containing a line containing one point. T …
Douglas Zare's user avatar