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arXiv · 2607.28664

Additive preservers of permanent rank

Alexander Guterman·Bojan Kuzma·Leonid Ovchinnikov
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Abstract

The permanent rank of a matrix $A$ is the size of the maximal square submatrix in $A$ which has a nonzero permanent. In this paper we characterize additive transformations $\Phi$ which preserve matrices of per-rank-one. Under an additional assumption that $\Phi$ is surjective or that it preserves per-rank-one in both directions we prove that $\Phi$ is a composition of a multiplication with diagonal matrices and permutation matrices from both sides, transposition, and injective endomorphism of the base field.

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Alexander Guterman, Bojan Kuzma, Leonid Ovchinnikov. 2026-07-24. Additive preservers of permanent rank. https://arxiv.org/abs/2607.28664

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