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  1. Eugène Ehrhart, Sur les polyèdres rationnels homothétiques à n dimensions, C. R. Acad. Sci. Paris 254 (1962), 616–618.

    MATH  MathSciNet  Google Scholar 

  2. Eugène Ehrhart, Sur les polyèdres homothétiques bordésà n dimensions, C. R. Acad. Sci. Paris 254 (1962), 988–990.

    MATH  MathSciNet  Google Scholar 

  3. Eugène Ehrhart, Sur un problème de géométrie diophantienne linéaire. I. Polyèdres et réseaux, J. Reine Angew. Math. 226 (1967), 1–29.

    MATH  MathSciNet  Google Scholar 

  4. Eugène Ehrhart, Sur un problème de géométrie diophantienne linéaire. II. Systèmes diophantiens linéaires, J. Reine Angew. Math. 227 (1967), 25–49.

    MATH  MathSciNet  Google Scholar 

  5. Eugène Ehrhart, Démonstration de la loi de réciprocité pour un polyèdre entier, C. R. Acad. Sci. Paris Sér. A–B 265 (1967), A5–A7.

    MathSciNet  Google Scholar 

  6. I. G. Macdonald, Polynomials associated with finite cell-complexes, J. London Math. Soc. (2) 4 (1971), 181–192.

    MATH  MathSciNet  Google Scholar 

  7. Ian G. Macdonald, The volume of a lattice polyhedron, Proc. Cambridge Philos. Soc. 59 (1963), 719–726.

    MATH  MathSciNet  Google Scholar 

  8. Robin Hartshorne, Residues and duality, Lecture Notes in Mathematics Vol. 20, Springer-Verlag, Berlin, 1966.

    Google Scholar 

  9. Masa-Nori Ishida, Torus embeddings and dualizing complexes, Tôhoku Math. J. (2) 32 (1980), no. 1, 111–146.

    MATH  MathSciNet  Google Scholar 

  10. Masa-Nori Ishida, The local cohomology groups of an affine semigroup ring, Algebraic geometry and commutative algebra in Honor of Masayaoshi Nagata, Vol. I, Kinokuniya, Tokyo, 1987, pp. 141–153.

    Google Scholar 

  11. Michel Brion, Points entiers dans les polyèdres convexes, Ann. Sci. École Norm. Sup. (4) 21 (1988), no. 4, 653–663.

    MATH  MathSciNet  Google Scholar 

  12. Michel Brion and Michèle Vergne, Residue formulae, vector partition functions and lattice points in rational polytopes, J. Amer. Math. Soc. 10 (1997), no. 4, 797–833.

    Article  MathSciNet  Google Scholar 

  13. Bernd Sturmfels, On vector partition functions, J. Combin. Theory Ser. A 72 (1995), no. 2, 302–309.

    Article  MATH  MathSciNet  Google Scholar 

  14. Michéle Vergne, Residue formulae for Verlinde sums, and for number of integral points in convex rational polytopes, European women in mathematics (Malta, 2001), World Scientific Publishing, River Edge, NJ, 2003, pp. 225–285.

    Google Scholar 

  15. Alexander I. Barvinok, A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed, Math. Oper. Res. 19 (1994), no. 4, 769–779.

    MATH  MathSciNet  Google Scholar 

  16. Alexander Barvinok and James E. Pommersheim, An algorithmic theory of lattice points in polyhedra, New perspectives in algebraic combinatorics (Berkeley, CA, 1996–97), Mathematical Sciences Research Institute Vol. 38, Cambridge University Press, Cambridge, 1999, pp. 91–147.

    Google Scholar 

  17. [DH3TY03]_J. A. De Loera, D. Haws, R. Hemmecke, P. Huggins, J. Tauzer, and R. Yoshida, A user guide for LattE v1.1 and Software package, 2003, available at http://www.math.ucdavis.edu/~latte.

    Google Scholar 

  18. Alexander Barvinok and Kevin Woods, Short rational generating functions for lattice point problems, J. Amer. Math. Soc. 16 (2003), no. 4, 957–979 (electronic).

    Article  MathSciNet  Google Scholar 

  19. [DH3SY03]_Jesus De Loera, David Haws, Raymond Hemmecke, Peter Huggins, Bernd Sturmfels, Ruriko Yoshida, Short rational functions for toric algebra and applications, preprint, 2003. arXiv:math.CO/0307350

    Google Scholar 

  20. Daniel Bump, Kwok-Kwong Choi, Pär Kurlberg, and Jeffrey Vaaler, A local Riemann hypothesis. I, Math. Zeit. 233 (2000), no. 1, 1–19.

    MathSciNet  Google Scholar 

  21. M. Beck, J. A. De Loera, M. Develin, J. Pfeifle, and R. P. Stanley, Coefficients and roots of Ehrhart polynomials, Contemp. Math., to appear, 2004. arXiv:math.CO/0402148

    Google Scholar 

  22. Michel Brion and Michèle Vergne, Residue formulae, vector partition functions and lattice points in rational polytopes, J. Amer. Math. Soc. 10 (1997), no. 4, 797–833. Proposition 3.1

    Article  MathSciNet  Google Scholar 

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(2005). Ehrhart polynomials. In: Combinatorial Commutative Algebra. Graduate Texts in Mathematics, vol 227. Springer, New York, NY. https://doi.org/10.1007/0-387-27103-1_12

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