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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on lattice-face polytopes and their Ehrhart polynomials


Author: Fu Liu
Journal: Proc. Amer. Math. Soc. 137 (2009), 3247-3258
MSC (2000): Primary 05A19; Secondary 52B20
Published electronically: May 14, 2009
MathSciNet review: 2515395
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Abstract: We remove an unnecessary restriction in the definition of lattice-face polytopes and show that with the new definition, the Ehrhart polynomial of a lattice-face polytope still has the property that each coefficient is the normalized volume of a projection of the original polytope. Furthermore, we show that the new family of lattice-face polytopes contains all possible combinatorial types of rational polytopes.


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Additional Information

Fu Liu
Affiliation: Department of Mathematics, University of California, One Shields Avenue, Davis, California 95616
Email: fuliu@math.ucdavis.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09897-9
PII: S 0002-9939(09)09897-9
Keywords: Ehrhart polynomial, lattice-face, polytope
Received by editor(s): October 29, 2008
Received by editor(s) in revised form: January 17, 2009
Published electronically: May 14, 2009
Communicated by: Jim Haglund
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.