On Counting Integral Points in a Convex Rational Polytope

References

  • Baldoni-Silva W., Vergne M. Residues formulae for volumes and Ehrhart polynomials of convex polytopes. (2001) . arXiv:math.CO/0103097 v1Google Scholar
  • Barvinok A. I. A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed. Math. Oper. Res. (1994) 19:769–779LinkGoogle Scholar
  • Barvinok A. I., Pommersheim J. E. An algorithmic theory of lattice points in polyhedra. New Perspectives in Algebraic Combinatorics. MSRI Publication (1999) 38:91–147Google Scholar
  • Beck M. Multidimensional Ehrhart reciprocity. J. Combin. Theory Ser. A. (2002) 97:187–194CrossrefGoogle Scholar
  • Beck M. Counting lattice points by means of the residue theorem. Ramanujan J. (2000) 4:399–310CrossrefGoogle Scholar
  • Beck M., Diaz R., Robins S. The Frobenius problem, rational polytopes, and Fourier-Dedekind sums. J. Number Theor. (2002) 96:1–21Google Scholar
  • Brion M. Points entiers dans les polyèdres convexes. Ann. Ecol. Norm. Sup. (Sér. 4) (1988) 21:653–663CrossrefGoogle Scholar
  • Brion M., Vergne M. Residue formulae, vector partition functions and lattice points in rational polytopes. J. Amer. Math. Soc. (1997) 10:797–833CrossrefGoogle Scholar
  • Ehrhart E. Sur un problème de géométrie diophantienne linéaire II. J. Reine Angewandte Math. (1967) 227:25–49Google Scholar
  • Hiriart-Urruty J-B., Lemarechal C.Convex Analysis and Minimization Algorithms I (1993) (Springer-Verlag, Berlin) CrossrefGoogle Scholar
  • Kantor J-M., Khovanskii A. 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
  • Kollár J. Sharp effective Nullstellensatz. J. Am. Math. Soc. (1988) 1:963–975CrossrefGoogle Scholar
  • Lasserre J. B., Zeron E. S. A Laplace transform algorithm for the volume of a convex polytope. J. ACM (2001) 48:1126–1140CrossrefGoogle Scholar
  • Pukhlikov A., Khovanskii A. A Riemann-Roch theorem for integrals and sums of quasipolynomials over virtual polytopes. St. Petersburg Math. J. (1993) 4:789–812Google Scholar
  • Schrijver A.Theory of Linear and Integer Programming (1986) (John Wiley & Sons, Chichester, U.K.) Google Scholar
  • Seidenberg A. Constructions in algebra. Trans. Am. Math. Soc. (1974) 197:273–313CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.