Computing parametric rational generating functions with a primal Barvinok algorithm

Details Computing parametric rational generating functions with a primal Barvinok algorithm Computing parametric rational generating functions with a primal Barvinok algorithm

2007-05-24

arxiv.org/abs/0705.3651v2

Mathematics

Combinatorics

16 pages, 1 figure; v2: Minor corrections, new example and summary of algorithm; submitted to journal

Scientific paper

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 half-open variants of the full-dimensional polyhedra in the identity. This gives rise to a practically efficient, parametric Barvinok algorithm in the primal space.

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