On the Linear Span of Lattice Points in a Parallelepiped

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References

  1. [1]

    L. Babai: The Fourier transform and equations over finite abelian groups, Lecture Notes, 1989.

    Google Scholar 

  2. [2]

    V. Batyrev and J. Hofscheier: A generalization of a theorem of G. K. White, arXiv:1004.3411 [math], April 2010.

    Google Scholar 

  3. [3]

    V. Batyrev and J. Hofscheier: Lattice polytopes, finite abelian subgroups in SL(n;C) and coding theory, arXiv: 1309.5312 [math], September 2013.

    Google Scholar 

  4. [4]

    M. Beck and S. Robins: Computing the Continuous Discretely: Integer-point Enumeration in Polyhedra, Springer Science & Business Media, November 2007.

    Google Scholar 

  5. [5]

    W. Bienia, L. Goddyn, P. Gvozdjak, A. Sebő and M. Tarsi: Flows, View Obstructions, and the Lonely Runner, Journal of Combinatorial Theory, Series B 72 (1998), 1–9.

    MATH  Google Scholar 

  6. [6]

    A. Borisov: Quotient singularities, integer ratios of factorials, and the Riemann Hypothesis, International Mathematics Research Notices, 2008:rnn052, 2008.

    Google Scholar 

  7. [7]

    K. Conrad: Characters of finite abelian groups, Lecture Notes, 2010.

    Google Scholar 

  8. [8]

    A. R. Fletcher: Inverting Reid’s exact plurigenera formula, Mathematische Annalen 284 (1989), 617–629.

    MathSciNet  Article  MATH  Google Scholar 

  9. [9]

    A. Higashitani, B. Nill and A. Tsuchiya: Gorenstein polytopes with trinomial h*-polynomials, arXiv:1503.05685 [math], March 2015.

    Google Scholar 

  10. [10]

    S. Lang: Cyclotomic Fields I and II, Springer New York, January 1990.

    Google Scholar 

  11. [11]

    H. Montgomery and R. C. Vaughan: Multiplicative number theory I: Classical theory, volume 97, Cambridge University Press, 2006.

    Google Scholar 

  12. [12]

    S. Mori: On 3-dimensional terminal singularities, Nagoya Mathematical Journal 98 (1985), 43–66.

    MathSciNet  Article  MATH  Google Scholar 

  13. [13]

    D. R. Morrison and G. Stevens: Terminal quotient singularities in dimensions three and four, Proceedings of the American Mathematical Society 90 (1984), 15–20.

    MathSciNet  Article  MATH  Google Scholar 

  14. [14]

    J. E. Reeve: On the volume of lattice polyhedra, Proceedings of the London Mathematical Society 3 (1957), 378–395.

    MathSciNet  Article  MATH  Google Scholar 

  15. [15]

    M. Reid: Young person’s guide to canonical singularities, Algebraic geometry, Bowdoin (1985), 345–414.

    Google Scholar 

  16. [16]

    B. Reznick: Lattice point simplices, Discrete Mathematics 60 (1986), 219–242.

    MathSciNet  Article  MATH  Google Scholar 

  17. [17]

    A. Sebő: An introduction to empty lattice simplices, in: Integer programming and combinatorial optimization, 400–414. Springer, 1999.

    Google Scholar 

  18. [18]

    A. Terras: Fourier Analysis on Finite Groups and Applications, Cambridge University Press, March 1999.

    Google Scholar 

  19. [19]

    G. K. White: Lattice tetrahedra, Canad. J. Math 16 (1964), 389–396.

    MathSciNet  Article  MATH  Google Scholar 

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Correspondence to Marcel Celaya.

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Celaya, M. On the Linear Span of Lattice Points in a Parallelepiped. Combinatorica 38, 1385–1413 (2018). https://doi.org/10.1007/s00493-017-3562-7

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Mathematics Subject Classification (2000)

  • 52B20
  • 52B05
  • 11M20