Geodesic
Computing parametric rational generating functions with a primal Barvinok algorithm
The electronic journal of combinatorics, Tome 15 (2008)
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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 practically efficient, parametric Barvinok algorithm in the primal space.
DOI : 10.37236/740
Classification : 52B45, 52B55, 52C07, 52C45, 68W30 
@article{10_37236_740,
     author = {Matthias K\"oppe and Sven Verdoolaege},
     title = {Computing parametric rational generating functions with a primal {Barvinok} algorithm},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/740},
     zbl = {1180.52014},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/740/}
}
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Matthias Köppe; Sven Verdoolaege. Computing parametric rational generating functions with a primal Barvinok algorithm. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/740

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