A Lower Bound Theorem for Ehrhart Polynomials of Convex Polytopes
نویسندگان
چکیده
منابع مشابه
Ehrhart polynomials of convex polytopes with small volumes
Let P ⊂ R be an integral convex polytope of dimension d and δ(P) = (δ0, δ1, . . . , δd) be its δ-vector. By using the known inequalities on δ-vectors, we classify the possible δ-vectors of convex polytopes of dimension d with P
متن کاملEhrhart polynomials of cyclic polytopes
Abstract. The Ehrhart polynomial of an integral convex polytope counts the number of lattice points in dilates of the polytope. In [1], the authors conjectured that for any cyclic polytope with integral parameters, the Ehrhart polynomial of it is equal to its volume plus the Ehrhart polynomial of its lower envelope and proved the case when the dimension d = 2. In our article, we prove the conje...
متن کاملEhrhart Polynomials of Matroid Polytopes and Polymatroids
We investigate properties of Ehrhart polynomials for matroid polytopes, independence matroid polytopes, and polymatroids. In the first half of the paper we prove that for fixed rank their Ehrhart polynomials are computable in polynomial time. The proof relies on the geometry of these polytopes as well as a new refined analysis of the evaluation of Todd polynomials. In the second half we discuss...
متن کاملEhrhart Polynomials of Lattice-face Polytopes
There is a simple formula for the Ehrhart polynomial of a cyclic polytope. The purpose of this paper is to show that the same formula holds for a more general class of polytopes, lattice-face polytopes. We develop a way of decomposing any d-dimensional simplex in general position into d! signed sets, each of which corresponds to a permutation in the symmetric group Sd, and reduce the problem of...
متن کاملThe Lower Bound Theorem for polytopes that approximate C-convex bodies
The face numbers of simplicial polytopes that approximate C-convex bodies in the Hausdorff metric is studied. Several structural results about the skeleta of such polytopes are studied and used to derive a lower bound theorem for this class of polytopes. This partially resolves a conjecture made by Kalai in 1994: if a sequence {Pn}n=0 of simplicial polytopes converges to a C-convex body in the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1994
ISSN: 0001-8708
DOI: 10.1006/aima.1994.1042