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For $A\in\mathbb{Z}^{m\times n}$ we investigate the behaviour of the number of lattice points in $P_A(b)=\{x\in\mathbb{R}^n:Ax\leq b\}$, depending on the varying vector $b$.
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1962
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Peter McMullen, Representations of polytopes and polyhedral sets , Geometriae Dedicate 2
1973
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Eva Linke, Rational Ehrhart quasi-polynomials , Journal of Combinatorial Theory, Series A 118
1978
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by same author, Lattice invariant valuations on rational polytopes , Archiv der Mathematik 31-1
1978
Earlier work this paper cites.
Wolfgang Dahmen and Charles A. Micchelli, The number of solutions to linear Diophantine equations and multivariate splines , Transactions of the American Mathematical Society 308
1988
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Rolf Schneider, Convex bodies: The Brunn-Minkowski Theory , Cambridge University Press, 1993
1993
Cited alongside, same era.
Bernd Sturmfels, On vector partition functions , Journal of Combinatorial Theory, Series A 72
1995
Cited alongside, same era.
Günter M. Ziegler, Lectures on polytopes , Springer, 1995
1995
Cited alongside, same era.
Matthias Beck, A closer look at lattice points in rational simplices , Electronic Journal of Combinatorics 6
1999
Cited alongside, same era.
John Mount, Fast unimodular counting , Combinatorics, Probability and Computing 9
2000
Cited alongside, same era.
by same author, Multidimensional ehrhart reciprocity , Journal of Combinatorial Theory, Series A 97
2002
Later among the works it cites.
Matthias Beck and Sinai Robins, Computing the Continuous Discretely , Springer, 2007
2007
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2010
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Zhiqiang Xu, Multivariate splines and polytopes , Journal of Approximation Theory 163
2011
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