We present a new tool to compute the number
fA (b)\phi_{\bf A} (b) of integer solutions to the
linear system
x ³ 0, A x = b,
x \geq 0, A x = b,
where the coefficients of
AA and
bb are integral.
fA (b)\phi_{\bf A} (b) is often described as a
vector partition function. Our methods use partial fraction expansions of Euler
s
generating function for
fA ()\phi_{\bf A} (\b). A special class of vector partition functions are Ehrhart
(quasi-)polynomials counting integer points in dilated polytopes.
Vector partition function - Ehrhart theory - Littlewood-Richardson - Kostant partition function - BZ-triangles