Embedding a set of rational points in lower dimensions

The rational points of a definable set

Let X ⊂ R be a set that is definable in an o-minimal expansion of R. This paper shows that, in a suitable sense, there are very few rational points of X that do not lie on some connected semialgebraic subset of X of positive dimension. 2000 Mathematics Subject Classification: 11G99, 03C64

Distribution of Rational Points: A Survey

Point-Set Embedding in Three Dimensions

Given a graph G with n vertices and m edges, and a set P of n points on a three-dimensional integer grid, the 3D Point-Set Embeddability problem is to determine a (three-dimensional) crossing-free drawing of G with vertices located at P and with edges drawn as polylines with bend-points at integer grid points. We solve a variant of the problem in which the points of P lie on a plane. The result...

Density of the Periodic Points in the Interval Set

The dynamical system (f,R) is introduced and some of its properties are investigated. It is proven that there is an invariant set Λ on which the periodic points of f are dense.

distribution of rational points: a survey