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arXiv · 2510.06959

Counting generating spaces of matrices

Markus Reineke
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Abstract

We prove that generating subspaces of matrix rings over finite fields are counted by polynomials. We use this result to define and study two-variable versions of polynomials counting isomorphism classes of absolutely irreducible representations of free algebras.

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Markus Reineke. 2025-10-08. Counting generating spaces of matrices. https://arxiv.org/abs/2510.06959

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