5. Vector Partition Functions and Hyperplanes

Problem 5.1.
Study the quasipolynomial leading coefficients for $2$row vector partition functions. Find efficient computational methods for finding these coefficients. 
Problem 5.2.
Let $A$ be a finite, real, linear hyperplane arrangement with isometric chambers. Is $A$ a Coxeter arrangment? 
Problem 5.3.
What is the easiest way to compute the pieces of a vector partition function? 
Problem 5.4.
onsider the $A_{n1}$ vector partition function. How many pieces are there? This is known for $n\leq 7$, and there is known lower bound of $2^{\lfloor \frac{n}{2}\rfloor}$.
 Understand why some polynomials factor nicely over the arrangement.
 Consider $q$analogues. In particular, the $q$ version of $(1,2,3,\cdots)$ is conjectured to grow at $e^{\theta(n^2)}$.
Cite this as: AimPL: Polyhedral geometry and partition theory, available at http://aimpl.org/polypartition.