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arXiv · 2201.09060

Solvability of orbit-finite systems of linear equations

Arka Ghosh·Piotr Hofman·Sławomir Lasota
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Abstract

We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under mild effectiveness assumptions, and reduces a given orbit-finite system to a number of finite ones: exponentially many in general, but polynomially many when atom dimension of input systems is fixed. Towards obtaining the procedure we push further the theory of vector spaces generated by orbit-finite sets, and show that each such vector space admits an orbit-finite basis. This fundamental property is a key tool in our development, but should be also of wider interest.

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Arka Ghosh, Piotr Hofman, Sławomir Lasota. 2022-01-22. Solvability of orbit-finite systems of linear equations. https://arxiv.org/abs/2201.09060

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