Effective lattice point counting in rational convex polytopes

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Exact sampling and counting for fixed-margin matrices (2013, methodology): “Regarding M(p,q), one of the most efficient algorithms known to date is LattE (Lattice point Enumeration) (De Loera et al., 2004), which uses the algorithm of Barvinok (1994) to count lattice points contained in convex polyhedra.”
Ehrhart polynomials and successive minima (2005, background): “[14, 15 ]). There were also some attempts to bound G(P) in terms of the intrinsic volumes (see [20, 43] as general references), but only with limited success.”
COEFFICIENTS AND ROOTS OF EHRHART POLYNOMIALS (2004, unknown): “Our investigations and conjectures are supported by computer experimentation using LattE [4, 5 ] and polymake [12].”
The many aspects of counting lattice points in polytopes (2005, methodology): “The first implementation of Barvinok’s algorithm was the software LattE developed at UC Davis [23,24].”
Short rational generating functions for lattice point problems (2002, background): “This interesting fact is, apparently, due to G. Denham [ D96 ].”
A generating function for all semi-magic squares and the volume of the Birkhoff polytope (2007, background): “Stanley that this project got started, after he alerted us that there was a really nice pattern in the data presented in Table 2 of [13].”