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Modular counting of integral points under sparse non-negativity

Given a polyhedron $$Ax\geq b$$ where every entry of $A,b$ are non-negative and $A\in\{0,1\}^{m\times n}$ and there are $O(1)$ (say $\leq8$) non-negative entries per row of $A$ is it possible to ...
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Bit complexity of Barvinok's algorithm

I have seen many references which state Barvinok's algorithm has polynomial time complexity for counting integer points of polytopes in fixed dimension. What exactly is this arithmetic complexity? ...
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