  Steingrimsson (2001) showed that the chromatic polynomial of a graph is the
Hilbert function of a relative Stanley-Reisner ideal. We approach this result
from the point of view of Ehrhart theory and give a sufficient criterion for
when the Ehrhart polynomial of a given relative polytopal complex is a Hilbert
function in Steingrimsson's sense. We use this result to establish that the
modular and integral flow and tension polynomials of a graph are Hilbert
functions.
