Isoperimetric Sets of Integers

摘要

The celebrated isoperimetric theorem says that the circle provides the least-perimeterway to enclose a given area. In this note we discuss a generalization which arose at adepartmental research seminar [1] and which moves the isoperimetric problem fromgeometry to number theory and combinatorics. Instead of Euclidean space, let's takethe set No of nonnegative integers.