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Coefficients and roots of Ehrhart polynomials
 IN INTEGER POINTS IN POLYHEDRA—GEOMETRY, NUMBER THEORY, ALGEBRA, OPTIMIZATION, VOLUME 374 OF CONTEMP. MATH
, 2005
"... The Ehrhart polynomial of a convex lattice polytope counts integer points in integral dilates of the polytope. We present new linear inequalities satisfied by the coefficients of Ehrhart polynomials and relate them to known inequalities. We also investigate the roots of Ehrhart polynomials. We pro ..."
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Cited by 27 (2 self)
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The Ehrhart polynomial of a convex lattice polytope counts integer points in integral dilates of the polytope. We present new linear inequalities satisfied by the coefficients of Ehrhart polynomials and relate them to known inequalities. We also investigate the roots of Ehrhart polynomials. We
Ehrhart polynomials of cyclic polytopes
 Journal of Combinatorial Theory Ser. A
, 409
"... 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 it ..."
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Cited by 5 (2 self)
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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
The Ehrhart polynomial of the Birkhoff polytope
 DISCRETE COMPUT. GEOM
, 2003
"... The n th Birkhoff polytope is the set of all doubly stochastic n × n matrices, that is, those matrices with nonnegative real coefficients in which every row and column sums to one. A wide open problem concerns the volumes of these polytopes, which have been known for n ≤ 8. We present a new, compl ..."
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Cited by 57 (10 self)
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, complexanalytic way to compute the Ehrhart polynomial of the Birkhoff polytope, that is, the function counting the integer points in the dilated polytope. One reason to be interested in this counting function is that the leading term of the Ehrhart polynomial is—up to a trivial factor—the volume
NOTES ON THE ROOTS OF EHRHART POLYNOMIALS
, 2006
"... We determine lattice polytopes of smallest volume with a given number of interior lattice points. We show that the Ehrhart polynomials of those with one interior lattice point have largest roots with norm of order n 2, where n is the dimension. This improves on the previously best known bound n an ..."
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Cited by 16 (2 self)
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We determine lattice polytopes of smallest volume with a given number of interior lattice points. We show that the Ehrhart polynomials of those with one interior lattice point have largest roots with norm of order n 2, where n is the dimension. This improves on the previously best known bound n
qanalogues of Ehrhart polynomials
, 2013
"... One considers weighted sums over points of lattice polytopes, where the weight of a point v is the monomial q λ(v) for some linear form λ. One proposes a qanalogue of the classical theory of Ehrhart series and Ehrhart polynomials, including Ehrhart reciprocity and involving evaluation at the qinte ..."
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One considers weighted sums over points of lattice polytopes, where the weight of a point v is the monomial q λ(v) for some linear form λ. One proposes a qanalogue of the classical theory of Ehrhart series and Ehrhart polynomials, including Ehrhart reciprocity and involving evaluation at the qintegers.
MIXED EHRHART POLYNOMIALS
"... Abstract. For lattice polytopes P1,..., Pk ⊆ Rd, Bihan (2014) introduced the discrete mixed volume DMV(P1,..., Pk) in analogy to the classical mixed volume. In this note we initiate the study of the associated mixed Ehrhart polynomial MEP1,...,Pk(n) = DMV(nP1,..., nPk). We study properties of this ..."
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Abstract. For lattice polytopes P1,..., Pk ⊆ Rd, Bihan (2014) introduced the discrete mixed volume DMV(P1,..., Pk) in analogy to the classical mixed volume. In this note we initiate the study of the associated mixed Ehrhart polynomial MEP1,...,Pk(n) = DMV(nP1,..., nPk). We study properties
EHRHART POLYNOMIAL AND MULTIPLICITY TUTTE POLYNOMIAL
, 2011
"... We prove that the Ehrhart polynomial of a zonotope is a specialization of the multiplicity Tutte polynomial introduced in [15]. We derive some formulae for the volume and the number of integer points of the zonotope. ..."
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We prove that the Ehrhart polynomial of a zonotope is a specialization of the multiplicity Tutte polynomial introduced in [15]. We derive some formulae for the volume and the number of integer points of the zonotope.
EHRHART POLYNOMIALS OF MATROID POLYTOPES AND POLYMATROIDS
, 2007
"... 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 w ..."
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Cited by 4 (2 self)
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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
Characteristic and Ehrhart Polynomials
, 2003
"... Let A be a subspace arrangement and let χ(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 χ(A, t) counts a certain set of lattice points. One can use this result to study t ..."
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Cited by 16 (2 self)
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the partial factorization of χ(A, t) over the integers and the coefficients of its expansion in various bases for the polynomial ring R[t]. Next we prove that the characteristic polynomial of any Weyl hyperplane arrangement can be expressed in terms of an Ehrhart quasipolynomial for its affine Weyl chamber
Results 1  10
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145