منابع مشابه
Dedekind–Carlitz Polynomials as Lattice-Point Enumerators in Rational Polyhedra
We study higher-dimensional analogs of the Dedekind–Carlitz polynomials c (u, v; a, b) := b−1 X
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We discuss topics related to lattice points in rational polyhedra, including efficient enumeration of lattice points, “short” generating functions for lattice points in rational polyhedra, relations to classical and higher-dimensional Dedekind sums, complexity of the Presburger arithmetic, efficient computations with rational functions, and others. Although the main slant is algorithmic, struct...
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We present Barvinok’s 1994 and 1999 algorithms for counting lattice points in polyhedra. 1. The 1994 algorithm In [2], Barvinok presents an algorithm that, for a fixed dimension d, calculates the number of integer points in a rational polyhedron. It is shown in [6] and [7] that the question can be reduced to counting the number of integer points in a k-dimensional simplex with integer vertices ...
متن کامل2-Lattice Polyhedra: Duality
This is the first in a series of papers that explores a class of polyhedra we call 2-lattice polyhedra. 2-Lattice polyhedra are a special class of lattice polyhedra that include network flow polyhedra, fractional matching polyhedra, matroid intersection polyhedra, the intersection of two polymatroids, etc. In this paper we show that the maximum sum of components of a vector in a 2-lattice polyh...
متن کاملLattice closures of polyhedra
Given P ⊂ R, a mixed integer set P I = P ∩ (Z × Rn−t), and a k-tuple of n-dimensional integral vectors (π1, . . . , πk) where the last n− t entries of each vector is zero, we consider the relaxation of P I obtained by taking the convex hull of points x in P for which π 1 x, . . . , π T k x are integral. We then define the k-dimensional lattice closure of P I to be the intersection of all such r...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1977
ISSN: 0022-314X
DOI: 10.1016/0022-314x(77)90004-x