## A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed.(English)Zbl 0821.90085

Summary: We prove that for any dimension $$d$$ there exists a polynomial time algorithm for counting integral points in polyhedra in the $$d$$- dimensional Euclidean space. Previously such algorithms were known for dimensions $$d= 1,2, 3$$, and 4 only.

### MSC:

 90C10 Integer programming 90C60 Abstract computational complexity for mathematical programming problems 52B12 Special polytopes (linear programming, centrally symmetric, etc.) 52C07 Lattices and convex bodies in $$n$$ dimensions (aspects of discrete geometry) 52B55 Computational aspects related to convexity
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