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A note on lattice-face polytopes and their Ehrhart polynomials
Author(s):
Fu
Liu
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3247-3258.
MSC (2000):
Primary 05A19;
Secondary 52B20
Posted:
May 14, 2009
MathSciNet review:
2515395
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References |
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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.
References:
-
- 1.
- A. Barvinok, Lattice points, polyhedra, and complexity, Geometric Combinatorics, IAS/Park City Mathematics Series 13, Amer. Math. Soc., Providence, RI, 2007, 19-62. MR 2383125
- 2.
- M. Beck and S. Robins, Computing the continuous discretely: Integer-point enumeration in polyhedra, Undergraduate Texts in Mathematics, Springer, New York, 2007. MR 2271992 (2007h:11119)
- 3.
- E. Ehrhart, Sur les polyèdres rationnels homothétiques à
 dimensions, C. R. Acad. Sci. Paris 254 (1962), 616-618. MR 0130860 (24:A714) - 4.
- F. Liu, Ehrhart polynomials of cyclic polytopes, Journal of Combinatorial Theory Ser. A 111 (2005), 111-127. MR 2144858 (2006a:05012)
- 5.
- -, Ehrhart polynomials of lattice-face polytopes, Transactions of the AMS 360 (2008), 3041-3069. MR 2379786 (2009a:52012)
- 6.
- R. P. Stanley, Enumerative combinatorics, vol. 1, Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge, 1997. MR 1442260 (98a:05001)
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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:
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
Posted:
May 14, 2009
Communicated by:
Jim Haglund
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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