INTERMEDIATE SUMS ON POLYHEDRA: COMPUTATION AND REAL EHRHART THEORY
نویسندگان
چکیده
منابع مشابه
Intermediate Sums on Polyhedra: Computation and Real Ehrhart Theory
We study intermediate sums, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math. Comp. 75 (2006), 1449–1466]. For a given semi-rational polytope p and a rational subspace L, we integrate a given polynomial function h over all lattice slices of the polytope p parallel to the subspace L and sum...
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Let σ be a simplex of RN with vertices in the integral lattice ZN . The number of lattice points of mσ (= {mα : α ∈ σ}) is a polynomial function L(σ,m) of m ≥ 0. In this paper we present: (i) a formula for the coefficients of the polynomial L(σ, t) in terms of the elementary symmetric functions; (ii) a hyperbolic cotangent expression for the generating functions of the sequence L(σ,m), m ≥ 0; (...
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We continue our study of intermediate sums over polyhedra, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasipolynomial of a rational simplex, Math. Comp. 75 (2006), 1449– 1466]. By well-known decompositions, it is sufficient to consider the case of affine cones s+c, where s is an arbitrary real vertex and c is a rational polyhed...
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This article concerns the computational problem of counting the lattice points inside convex polytopes, when each point must be counted with a weight associated to it. We describe an efficient algorithm for computing the highest degree coefficients of the weighted Ehrhart quasi-polynomial for a rational simple polytope in varying dimension, when the weights of the lattice points are given by a ...
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ژورنال
عنوان ژورنال: Mathematika
سال: 2012
ISSN: 0025-5793,2041-7942
DOI: 10.1112/s0025579312000101