An algebraic-perturbation variant of Barvinok's algorithm

Jon Lee, Daphne E Skipper

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We give a variant of Barvinok's algorithm for computing a short rational generating function for the integer points in P := {x ∈ Rn : Ax ≤ b}; a use of which is to count the number of integer points in P. We use an algebraic perturbation, replacing each bi with bii, 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 languageEnglish (US)
Pages (from-to)15-20
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume50
DOIs
StatePublished - Dec 1 2015

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Integer Points
Rational functions
Polynomials
Perturbation
Polyhedron
Rational function
Generating Function
Count
Ring
Polynomial
Computing

Keywords

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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

An algebraic-perturbation variant of Barvinok's algorithm. / Lee, Jon; Skipper, Daphne E.

In: Electronic Notes in Discrete Mathematics, Vol. 50, 01.12.2015, p. 15-20.

Research output: Contribution to journalArticle

Lee, Jon ; Skipper, Daphne E. / An algebraic-perturbation variant of Barvinok's algorithm. In: Electronic Notes in Discrete Mathematics. 2015 ; Vol. 50. pp. 15-20.
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