An Alternative Algorithm for Counting Lattice Points in a Convex Polytope

Authors:
Jean B. Lasserre;Eduardo S. Zeron
Affiliations:
LAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cédex 4, France;Mathematics Department, CINVESTAV-IPN, Apdo. Postal 14-740, Mexico, D.F. 07000, Mexico
Venue:
Mathematics of Operations Research
Year:
2005

Citing 4
Cited 2

Theory of linear and integer programming

Theory of linear and integer programming
Residue formulae for vector partitions and Euler--MacLaurin sums

Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
On Counting Integral Points in a Convex Rational Polytope

Mathematics of Operations Research
Counting Integer Flows in Networks

Foundations of Computational Mathematics

Simple Explicit Formula for Counting Lattice Points of Polyhedra

IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
On the bit-complexity of sparse polynomial and series multiplication

Journal of Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We provide an alternative algorithm for counting lattice points in the convex polytope {x â聢聢 â聞聺nâ聢拢Ax = b, x â聣楼 0}. It is based on an exact (tractable) formula for the case A â聢聢 â聞陇míï戮聴(m+1) that we repeatedly use for the general case A â聢聢 â聞陇míï戮聴n.