2007
DOI: 10.1007/s00454-007-1330-y
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Notes on the Roots of Ehrhart Polynomials

Abstract: Abstract. We determine lattice polytopes of smallest volume with a given number of interior lattice points. We show that the Ehrhart polynomials of those with one interior lattice point have largest roots with norm of order n 2 , where n is the dimension. This improves on the previously best known bound n and complements a recent result of Braun [8] where it is shown that the norm of a root of a Ehrhart polynomial is at most of order n 2 .For the class of 0-symmetric lattice polytopes we present a conjecture … Show more

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Cited by 51 publications
(53 citation statements)
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“…Furthermore, the roots of Ehrhart polynomials are also an object of intensive studies [6,9,12,20]. There are many graphs for which these roots have a remarkable property: They lie on a line R = {z : Re(z) = − 1 2 }.…”
Section: Introductionmentioning
confidence: 99%
“…Furthermore, the roots of Ehrhart polynomials are also an object of intensive studies [6,9,12,20]. There are many graphs for which these roots have a remarkable property: They lie on a line R = {z : Re(z) = − 1 2 }.…”
Section: Introductionmentioning
confidence: 99%
“…The roots of an Ehrhart polynomial should also reflect properties of a polytope that are hard to elicit just from the coefficients. Among the many papers on the topic, including [4], [5], [6], [12] and [23], Beck et al [3] conjecture that: Compared with the norm bound, which is O(D 2 ) in general [5], the strip in the conjecture puts a tight restriction on the distribution of roots for any Ehrhart polynomial.…”
Section: Introductionmentioning
confidence: 99%
“…Recently, many research papers on convex polytopes, including [2], [3], [4], [5], [8], [9] and [18], discuss roots of Ehrhart polynomials. One of the fascinating topics is the study on roots of Ehrhart polynomials of Gorenstein Fano polytopes.…”
Section: Roots Of Ehrhart Polynomials Of Gorenstein Fano Polytopesmentioning
confidence: 99%