An upper bound theorem concerning lattice polytopes

Gábor Hegedüs

doi:10.1556/012.2015.52.3.1314

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 52: Issue 3

An upper bound theorem concerning lattice polytopes

Author:

Gábor Hegedüs

Gábor Hegedüs Óbuda University, Antal Bejczy Center for Intelligent Robotics Kiscelli u. 82, 1032 Budapest, Hungary

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Pages:: 337–349

Online Publication Date:: Sep 2015

Publication Date:: 01 Sep 2015

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/012.2015.52.3.1314

Keywords:: Primary 52B20; Secondary 13A02; 05E40; Lattice polytope; integrally closed polytope; Cohen–Macaulay ring

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R. P. Stanley proved the Upper Bound Conjecture in 1975. We imitate his proof for the Ehrhart rings.

We give some upper bounds for the volume of integrally closed lattice polytopes. We derive some inequalities for the δ-vector of integrally closed lattice polytopes. Finally we apply our results for reflexive integrally closed and order polytopes.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

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János PACH (Rényi Institute of Mathematics)
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Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
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