Counting generating spaces of matrices

Published 8 Oct 2025 in math.RT and math.RA | (2510.06959v1)

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

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