Strengthens the solvability of Mx=diag(M) for symmetric M over F2 to a parity rigidity theorem diag(M)^T x ≡ rank(M) mod 2, with rank-update formulas and tree recursions for generalized odd-domination.
Symmetric Matrices over F_2 and the Lights Out Problem
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
We prove that the range of a symmetric matrix over F_2 contains the vector of its diagonal elements. We apply the theorem to a generalization of the "Lights Out" problem on graphs.
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math.CO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Diagonal parity and loop toggling for symmetric matrices over $\mathbb F_2$
Strengthens the solvability of Mx=diag(M) for symmetric M over F2 to a parity rigidity theorem diag(M)^T x ≡ rank(M) mod 2, with rank-update formulas and tree recursions for generalized odd-domination.