  This set of notes is based on a lecture I gave at "50 years of Finite
Geometry | A conference on the occasion of Jef Thas's 70th birthday," in
November 2014. It consists essentially of three parts: in a first part, I
introduce some ideas which are based in the combinatorial theory underlying
$\mathbb{F}_1$, the field with one element. In a second part, I describe, in a
nutshell, the fundamental scheme theory over $\mathbb{F}_1$ which was designed
by Deitmar. The last part focuses on zeta functions of Deitmar schemes, and
also presents more recent work done in this area.
