Ehrhart polynomials of lattice-face polytopes
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- by Fu Liu PDF
- Trans. Amer. Math. Soc. 360 (2008), 3041-3069 Request permission
Abstract:
There is a simple formula for the Ehrhart polynomial of a cyclic polytope. The purpose of this paper is to show that the same formula holds for a more general class of polytopes, lattice-face polytopes. We develop a way of decomposing any $d$-dimensional simplex in general position into $d!$ signed sets, each of which corresponds to a permutation in the symmetric group $\mathfrak S_d,$ and reduce the problem of counting lattice points in a polytope in general position to that of counting lattice points in these special signed sets. Applying this decomposition to a lattice-face simplex, we obtain signed sets with special properties that allow us to count the number of lattice points inside them. We are thus able to conclude the desired formula for the Ehrhart polynomials of lattice-face polytopes.References
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Additional Information
- Fu Liu
- Affiliation: Department of Mathematics, Room 2-333, 77 Massachusetts Avenue, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- Address at time of publication: Department of Mathematics, University of California, Davis, One Shields Avenue, Davis, California 95616
- ORCID: 0000-0003-0497-4083
- Email: fuliu@math.mit.edu, fuliu@math.ucdavis.edu
- Received by editor(s): February 15, 2006
- Received by editor(s) in revised form: March 15, 2006
- Published electronically: January 8, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 3041-3069
- MSC (2000): Primary 05A19; Secondary 52B20
- DOI: https://doi.org/10.1090/S0002-9947-08-04288-8
- MathSciNet review: 2379786