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
An Alternative Algorithm for Counting Lattice Points in a Convex Polytope
Mathematics of Operations Research
| Hi-index | 0.00 |
Given z茂戮驴 茂戮驴nand A茂戮驴 茂戮驴m×n, we provide an explicit expression and an algorithm for evaluating the counting function h(y;z): = 茂戮驴 { zx| x茂戮驴 茂戮驴n;Ax=y,x茂戮驴 0}. The algorithm only involves simple (but possibly numerous) calculations. In addition, we exhibit finitely manyfixed convex cones of 茂戮驴nexplicitly and exclusively defined by A, such that for anyy茂戮驴 茂戮驴m, h(y;z) is obtained by a simple formula that evaluates 茂戮驴 zxover the integral points of those cones only. At last, we also provide an alternative (and different) formula from a decomposition of the generating function into simpler rational fractions, easy to invert.