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An Alternative Algorithm for Counting Lattice Points in a Convex Polytope

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
lasserre{at}laas.fr, www.laas.fr/~lasserre
eszeron{at}math.cinvestav.mx

We provide an alternative algorithm for counting lattice points in the convex polytope {x ⁿ | Ax = b, x 0}. It is based on an exact (tractable) formula for the case A ^mx(m+1) that we repeatedly use for the general case A ^mxn.

Key Words: convex polytopes; lattice points; generating functions; counting lattice points
History: Received: November 13, 2004; revision received: July 9, 2004;revision received: October 1, 2004;