For every polynomial with positive coefficients, all sufficiently large dilations are magic positive, and the paper introduces the m-index to measure this threshold for Ehrhart polynomials of polytopes.
Norm bounds for Ehrhart polynomial roots
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On the magic positivity of Ehrhart polynomials of dilated polytopes
For every polynomial with positive coefficients, all sufficiently large dilations are magic positive, and the paper introduces the m-index to measure this threshold for Ehrhart polynomials of polytopes.