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On the coefficients of Hilbert quasipolynomials


Authors: Winfried Bruns and Bogdan Ichim
Journal: Proc. Amer. Math. Soc. 135 (2007), 1305-1308
MSC (2000): Primary 13A02
DOI: https://doi.org/10.1090/S0002-9939-06-08834-4
Published electronically: November 15, 2006
MathSciNet review: 2276638
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Abstract: The Hilbert function of a module over a positively graded algebra is of quasi-polynomial type (Hilbert-Serre). We derive an upper bound for its grade, i.e. the index from which on its coefficients are constant. As an application, we give a purely algebraic proof of an old combinatorial result (due to Ehrhart, McMullen and Stanley).


References [Enhancements On Off] (What's this?)

  • [BH] W. Bruns and J. Herzog. Cohen-Macaulay Rings. Rev. ed. Cambridge University Press, 1998.
  • [E] E. Ehrhart, Polynômes arithmétiques et méthode des polyèdres en combinatoire, Birkhäuser Verlag, Basel-Stuttgart, 1977. International Series of Numerical Mathematics, Vol. 35. MR 0432556
  • [M] P. McMullen. Lattice invariant valuations on rational polytopes. Arch. Math. 31 (1978/79), 509-516. MR 0526617 (80d:52011)
  • [S] R. Stanley. Decompositions of rational convex polytopes. Ann. Discr. Math. 6 (1980), 333-342. MR 0593545 (82a:52007)

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Additional Information

Winfried Bruns
Affiliation: FB Mathematik/Informatik, Universität Osnabrück, 49069 Osnabrück, Germany
Email: winfried@math.uos.de

Bogdan Ichim
Affiliation: FB Mathematik/Informatik, Universität Osnabrück, 49069 Osnabrück, Germany; and Institute of Mathematics, C.P. 1-764, 70700 Bucharest, Romania
Email: bogdan.ichim@math.uos.de; bogdan.ichim@imar.ro

DOI: https://doi.org/10.1090/S0002-9939-06-08834-4
Keywords: Hilbert quasi-polynomial, Ehrhart quasi-polynomial
Received by editor(s): December 22, 2005
Published electronically: November 15, 2006
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2006 American Mathematical Society

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