Abstract: Our project is about counting integer points in polyhedra.
A matrix $A\in M_{d\times n}$ defines a polyhedra
$P_b^A:=\left\{ x\in \mathbb{R}_{\geq 0}^n: Ax=b\right\}$.
The so-called vector partition function for
$A$ is $\phi^A(b):= \#\left( P_b^A \cap \mathbb{Z}^n\right)$.
A theorem of Sturmfels says that $\phi^A(b)$ is given by several
polynomials in $b$. In the lecture I will discuss a method to compute
$\phi^A(b)$. Then I will show the computation of the polynomials for an
example which gives Kostants' partition function for type $C2.$
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