Parametric Polyhedra with at least $k$ Lattice Points: Their Semigroup Structure and the k-Frobenius Problem

Iskander Aliev, Jesus A. De Loera, Quentin Louveaux

Given an integral $d\times n$ matrix $A$, the well-studied affine semigroup $\mbox{ Sg} (A)=\{ b : Ax=b, \ x \in {\mathbb Z}^n, x \geq 0\}$ can be stratified by the number of latt…