89 citations · 338 across the 44 of their papers we have counts for
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Spanning Lattice Polytopes and the Uniform Position Principle
Johannes Hofscheier, Lukas Katthän, Benjamin Nill
A lattice polytope is called IDP if any lattice point in its th dilate is a sum of lattice points in . In 1991 Stanley proved a strong inequality in Ehrhart theory fo…
Lattice simplices with a fixed positive number of interior lattice points: A nearly optimal volume bound
Gennadiy Averkov, Jan Krümpelmann, Benjamin Nill
We give an explicit upper bound on the volume of lattice simplices with fixed positive number of interior lattice points. The bound differs from the conjectural sharp upper bound o…
The mixed degree of families of lattice polytopes
Benjamin Nill
The degree of a lattice polytope is a notion in Ehrhart theory that was studied quite intensively over the previous years. It is well-known that a lattice polytope has normalized v…
Smooth polytopes with negative Ehrhart coefficients
Federico Castillo, Fu Liu, Benjamin Nill +1
We present examples of smooth lattice polytopes in dimensions 3 and higher where each coefficient of their Ehrhart polynomials that can potentially be negative is indeed negative.…