### Abstract

We give a variant of Barvinok's algorithm for computing a short rational generating function for the integer points in P := {x ∈ R^{n} : Ax ≤ b}; a use of which is to count the number of integer points in P. We use an algebraic perturbation, replacing each b_{i} with b_{i}+τ^{i}, where τ>0 is an arbitrarily small indeterminate. Hence, our new right-hand vector has components in the ordered ring Q[τ] of polynomials in τ. Denoting the perturbed polyhedron by P(τ)⊂R[τ]^{n}, we use the facts that: P(τ) is full dimensional, simple, and contains the same integer points as P.

Original language | English (US) |
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Pages (from-to) | 15-20 |

Number of pages | 6 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 50 |

DOIs | |

State | Published - Dec 1 2015 |

### Keywords

- Barvinok's algorithm
- Generating function
- Integer
- Polyhedron

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

Lee, J., & Skipper, D. (2015). An algebraic-perturbation variant of Barvinok's algorithm.

*Electronic Notes in Discrete Mathematics*,*50*, 15-20. https://doi.org/10.1016/j.endm.2015.07.004