On Counting Integral Points in a Convex Rational Polytope
Published Online:1 Nov 2003https://doi.org/10.1287/moor.28.4.853.20518
References
- Residues formulae for volumes and Ehrhart polynomials of convex polytopes. (2001) . arXiv:math.CO/0103097 v1Google Scholar
- A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed. Math. Oper. Res. (1994) 19:769–779Link, Google Scholar
- An algorithmic theory of lattice points in polyhedra. New Perspectives in Algebraic Combinatorics. MSRI Publication (1999) 38:91–147Google Scholar
- Multidimensional Ehrhart reciprocity. J. Combin. Theory Ser. A. (2002) 97:187–194Crossref, Google Scholar
- Counting lattice points by means of the residue theorem. Ramanujan J. (2000) 4:399–310Crossref, Google Scholar
- The Frobenius problem, rational polytopes, and Fourier-Dedekind sums. J. Number Theor. (2002) 96:1–21Google Scholar
- Points entiers dans les polyèdres convexes. Ann. Ecol. Norm. Sup. (Sér. 4) (1988) 21:653–663Crossref, Google Scholar
- Residue formulae, vector partition functions and lattice points in rational polytopes. J. Amer. Math. Soc. (1997) 10:797–833Crossref, Google Scholar
- Sur un problème de géométrie diophantienne linéaire II. J. Reine Angewandte Math. (1967) 227:25–49Google Scholar
- Convex Analysis and Minimization Algorithms I (1993) (Springer-Verlag, Berlin) Crossref, Google Scholar
- Une application du théorème de Riemann-Roch combinatoire au polynôme d'Ehrhart des polytopes entiers. C.R. Acad. Sci. Paris (Série I) (1993) 317:501–507Google Scholar
- Sharp effective Nullstellensatz. J. Am. Math. Soc. (1988) 1:963–975Crossref, Google Scholar
- A Laplace transform algorithm for the volume of a convex polytope. J. ACM (2001) 48:1126–1140Crossref, Google Scholar
- A Riemann-Roch theorem for integrals and sums of quasipolynomials over virtual polytopes. St. Petersburg Math. J. (1993) 4:789–812Google Scholar
- Theory of Linear and Integer Programming (1986) (John Wiley & Sons, Chichester, U.K.) Google Scholar
- Constructions in algebra. Trans. Am. Math. Soc. (1974) 197:273–313Crossref, Google Scholar

