All Questions

For a convex polygon $P$, draw all the diagonals of $P$ and consider the intersection points made by those diagonals. Let $f(n)$ be the minimal number of such intersections where $P$ ranges over all ...

Suppose I am given a projective plane $P \cong \mathbb{P}^2(k)$ over a (commutative) field $k$. With "projective plane," I mean the point-line geometry (and not, for instance, the scheme): $...

Consider $9n$ pencils through non-collinear points $p_1, \ldots , p_{9n}$ in $R^2$ each consisting of at most $n$ concurrent lines. Define the intersection $S$ of these pencils to be the set of points ...

I was reading Adam Sheffer's book "Polynomial Methods and Incidence Theory" and I tried to solve the following exercise: Exercise 1.1 Construct a set $\mathcal{P}$ of $m$ points and a set $\...