Electronic Journal of Combinatorics vol:15 issue:1 pages:R16
Computations with Barvinok's short rational generating functions are
traditionally being performed in the dual space, to avoid the combinatorial complexity
of inclusion--exclusion formulas for the intersecting proper faces of cones.
We prove that, on the level of indicator functions of polyhedra,
there is no need for using inclusion--exclusion formulas to
account for boundary effects: All linear identities in the space of
indicator functions can be purely expressed using partially open variants of the
full-dimensional polyhedra in the identity. This gives rise to a
parametric Barvinok algorithm in the primal space.