Geodesic
On counterexamples to a conjecture of Wills and Ehrhart polynomials whose roots have equal real parts
Matthias Henze1
1Institut für Informatik Freie Universität Berlin Berlin, Germany
The electronic journal of combinatorics, Tome 21 (2014) no. 1
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As a discrete analog to Minkowski's theorem on convex bodies, Wills conjectured that the Ehrhart coefficients of a $0$-symmetric lattice polytope with exactly one interior lattice point are maximized by those of the cube of side length two. We discuss several counterexamples to this conjecture and, on the positive side, we identify a family of lattice polytopes that fulfill the claimed inequalities. This family is related to the recently introduced class of $l$-reflexive polytopes.
DOI : 10.37236/3757
Classification : 52B20, 11H06, 52A40
Mots-clés : Ehrhart polynomial, \(l\)-reflexive polytope, lattice polytope, Wills' conjecture

Matthias Henze  1

1 Institut für Informatik Freie Universität Berlin Berlin, Germany 
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     title = {On counterexamples to a conjecture of {Wills} and {Ehrhart} polynomials whose roots have equal real parts},
     journal = {The electronic journal of combinatorics},
     year = {2014},
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     number = {1},
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Matthias Henze. On counterexamples to a conjecture of Wills and Ehrhart polynomials whose roots have equal real parts. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3757

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