Computing parametric rational generating functions with a primal Barvinok algorithm
Combinatorics
2017-01-03 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0705.3651,
title = {Computing parametric rational generating functions with a primal Barvinok algorithm},
author = {Matthias Köppe and Sven Verdoolaege},
journal= {arXiv preprint arXiv:0705.3651},
year = {2017}
}