Theoretical computer science · Oct 6, 2026

A cubic permanent–determinant lower bound

Proves an Ω(n3)\Omega(n^3) lower bound for the border determinantal complexity of the n×nn\times n permanent over ℂ. Even coefficientwise limits of determinants of affine-linear matrices require matrix size at least cn3cn^3, for an absolute c > 0 and all sufficiently large n; the same bound therefore holds for exact representations.

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