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arXiv · 2610.37616

Generic tensor products are not maximal

Mykhaylo Tyomkyn
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Abstract

We construct tensor products of uniform matroids which are strictly freer than their generic linear tensor products. In particular, the generic tensor product of two copies of $U_{7,9}$ is not maximal. More generally, for every $a,b\ge2$, this holds for $U_{7,a+7}$ and $U_{7,b+7}$. The construction disproves the uniform tensor-product formulation of Mason's conjecture. Its dual is a relaxation of an explicit circuit-hyperplane of a generic birigidity matroid. By the author's representability theorem, the resulting matroids are non-representable over every field. We also obtain full-rank counterexamples to the Jackson--Tanigawa hyperconnectivity conjecture in every dimension $d\ge2$.

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Mykhaylo Tyomkyn. 2026-10-27. Generic tensor products are not maximal. https://arxiv.org/abs/2610.37616

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