Please use this identifier to cite or link to this item: http://hdl.handle.net/1783.1/3144
Lattice points, Dedekind sums, and Ehrhart polynomials of lattice polyhedra
Authors  Chen, BF  

Issue Date  2002  
Source  Discrete & Computational Geometry, v. 28, (2), 2002, SEP, p. 175199  
Summary  Let a be a simplex of RN with vertices in the integral lattice Z(N). The number of lattice points of msigma (= {malpha: alpha is an element of sigma}) is a polynomial function L(sigma, m) of m greater than or equal to 0. In this paper we present: (i) a formula for the coefficients of the polynomial L(sigma, t) in terms of the elementary symmetric functions; (ii) a hyperbolic cotangent expression for the generating functions of the sequence L(sigma, m), m greater than or equal to 0; (iii) an explicit formula for the coefficients of the polynomial L (sigma, t) in terms of torsion. As an application of (i), the coefficient for the lattice nsimplex of Rn with the vertices (0,..., 0, a(j), 0,..., 0) (1 less than or equal to j less than or equal to 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 selfcontained.  
Subjects  
ISSN  01795376  
Rights  The original publication is available at http://www.springerlink.com  
Language  English 

Format  Article  
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