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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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Fu Liu
Affiliation: Department of Mathematics, University of California, One Shields Avenue, Davis, California 95616

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.

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