منابع مشابه
Generalized Ehrhart Polynomials
Let P be a polytope with rational vertices. A classical theorem of Ehrhart states that the number of lattice points in the dilations P (n) = nP is a quasi-polynomial in n. We generalize this theorem by allowing the vertices of P (n) to be arbitrary rational functions in n. In this case we prove that the number of lattice points in P (n) is a quasi-polynomial for n sufficiently large. Our work w...
متن کاملMixed Ehrhart polynomials
For lattice polytopes P1, . . . , Pk ⊆ Rd, Bihan (2016) introduced the discrete mixed volume DMV(P1, . . . , Pk) in analogy to the classical mixed volume. In this note we study the associated mixed Ehrhart polynomial MEP1,...,Pk(n) = DMV(nP1, . . . , nPk). We provide a characterization of all mixed Ehrhart coefficients in terms of the classical multivariate Ehrhart polynomial. Bihan (2016) show...
متن کاملCharacteristic and Ehrhart Polynomials
Let A be a subspace arrangement and let (A; t) be the characteristic polynomial of its intersection lattice L(A). We show that if the subspaces in A are taken from L(Bn), where Bn is the type B Weyl arrangement, then (A; t) counts a certain set of lattice points. This is the only known combinatorial interpretation of this polynomial in the subspace case. One can use this result to study the par...
متن کاملq-analogues of Ehrhart polynomials
One considers weighted sums over points of lattice polytopes, where the weight of a point v is the monomial q for some linear form λ. One proposes a q-analogue of the classical theory of Ehrhart series and Ehrhart polynomials, including Ehrhart reciprocity and involving evaluation at the q-integers.
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...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2012
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2011-05494-2