PreprintarXiv licencearXiv
Generic tensor products are not maximal
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 U7,9 is not maximal. More generally, for every a,b≥2, this holds for U7,a+7 and U7,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≥2.
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BibTeX
@misc{tyomkyn2026generic,
title = {{Generic tensor products are not maximal}},
author = {Mykhaylo Tyomkyn},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37616},
eprint = {2610.37616},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37616},
}
RIS
TY - UNPB
TI - Generic tensor products are not maximal
AU - Mykhaylo Tyomkyn
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37616
UR - https://arxiv.org/abs/2610.37616
AB - 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≥2, 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≥2.
ER -