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arXiv · 2611.03636

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Radu Curticapean
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Abstract

We show that $n \times n$ permanents can be computed with $O^*{(2-\varepsilon)^n}$ arithmetic operations over every commutative ring, for $\varepsilon = 10^{-40}$. This solves a problem stated in Knuth's The Art of Computer Programming. Our algorithm implements the classical Binet--Minc identity with dynamic programming and careful bookkeeping. It also gives algebraic branching programs of size $O^*{(2-\varepsilon)^n}$.

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Radu Curticapean. 2026-11-02. Get Permanent Results Faster by Counting Stars. https://arxiv.org/abs/2611.03636

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