On the coefficients of Hilbert quasipolynomials
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- by Winfried Bruns and Bogdan Ichim PDF
- Proc. Amer. Math. Soc. 135 (2007), 1305-1308 Request permission
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
- W. Bruns and J. Herzog. Cohen-Macaulay Rings. Rev. ed. Cambridge University Press, 1998.
- E. Ehrhart, Polynômes arithmétiques et méthode des polyèdres en combinatoire, International Series of Numerical Mathematics, Vol. 35, Birkhäuser Verlag, Basel-Stuttgart, 1977. MR 0432556
- P. McMullen, Lattice invariant valuations on rational polytopes, Arch. Math. (Basel) 31 (1978/79), no. 5, 509–516. MR 526617, DOI 10.1007/BF01226481
- Richard P. Stanley, Decompositions of rational convex polytopes, Ann. Discrete Math. 6 (1980), 333–342. MR 593545, DOI 10.1016/S0167-5060(08)70717-9
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
- Received by editor(s): December 22, 2005
- Published electronically: November 15, 2006
- Communicated by: Bernd Ulrich
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 1305-1308
- MSC (2000): Primary 13A02
- DOI: https://doi.org/10.1090/S0002-9939-06-08834-4
- MathSciNet review: 2276638