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Please use this identifier to cite or link to this item: http://hdl.handle.net/1783.1/3144
Title: Lattice points, Dedekind sums, and Ehrhart polynomials of lattice polyhedra
Authors: Chen, Bei-fang
Keywords: Lattice points
Dedekind sums
Ehrhart polynomials
Lattice polytopes
Issue Date: Mar-2002
Citation: Discrete. Comput. Geom. 28(2) (2002) 175–199.
Abstract: 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; (iii) an explicit formula for the coefficients of the polynomial L(σ; t) in terms of torsion. As an application of (i), the coefficient for the lattice n-simplex of Rn with the vertices (0,...,0,aj,0,...,0) (1 ≤ j ≤ n) plus the origin is explicitly expressed in terms of Dedekind sums; and when n = 2, it reduces to the reciprocity law about Dedekind sums. The whole exposition is elementary and self-contained.
Rights: The original publication is available at http://www.springerlink.com
URI: http://hdl.handle.net/1783.1/3144
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