The Hilbert basis of a convex cone C is a minimal set of integer vectorss in C such that every integer vector in C is a conical combination of the vectors in the Hilbert basis with integer coefficients.

Definition

Given a lattice

we consider the monoid. By Gordan's lemma, this monoid is finitely generated, i.e., there exists a finite set is an integer conical combination of these points:

The cone C—the Hilbert basis of C.

References