Roots of Ehrhart Polynomials of Smooth Fano Polytopes

V. Golyshev conjectured that for any smooth polytope P with dim( P )≤5 the roots z ∈ℂ of the Ehrhart polynomial for P have real part equal to −1/2. An elementary proof is given, and in each dimension the roots are described explicitly. We also present examples which demonstrate that this result cann...

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Bibliographic Details
Published in:Discrete & computational geometry 2011-10, Vol.46 (3), p.488-499
Main Authors: Hegedüs, Gábor, Kasprzyk, Alexander M.
Format: Article
Language:English
Subjects:
Combinatorics
Computational geometry
Computational mathematics
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Polynomials
Polytopes
Proving
Roots
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Summary:V. Golyshev conjectured that for any smooth polytope P with dim( P )≤5 the roots z ∈ℂ of the Ehrhart polynomial for P have real part equal to −1/2. An elementary proof is given, and in each dimension the roots are described explicitly. We also present examples which demonstrate that this result cannot be extended to dimension six.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-010-9275-y