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On the coefficients of Hilbert quasipolynomials
Author(s):
Winfried
Bruns;
Bogdan
Ichim
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1305-1308.
MSC (2000):
Primary 13A02
Posted:
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:
-
- [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. International Series of Numerical Mathematics. 35, Birkhäuser Verlag, 1977. MR 0432556 (55:5544)
- [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:
10.1090/S0002-9939-06-08834-4
PII:
S 0002-9939(06)08834-4
Keywords:
Hilbert quasi-polynomial,
Ehrhart quasi-polynomial
Received by editor(s):
December 22, 2005
Posted:
November 15, 2006
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2006,
American Mathematical Society
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