Represented Tensor Products of Binary Matroids
Abstract
For binary matroids M,N representable over a common field F, the Kronecker product of their F-representations defines a matroid TF(M,N) independent of the chosen representations. We classify when this represented tensor product is regular, cographic, graphic, or binary. For simple nonfree factors, regularity holds exactly when, up to interchange, one factor is a cactus matroid and the other is outerplanar, or one is a triangular cactus matroid and the other is series--parallel. Cographicity holds exactly in the first case. For simple factors with nonempty ground sets, graphicity holds exactly when one factor is free and the other is graphic. For fixed factors, regularity, cographicity, and graphicity are independent of the common representation field, although the isomorphism type may vary with its characteristic. Products of at least three simple nonfree factors are nonregular.
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BibTeX
@misc{fu2026represented,
title = {{Represented Tensor Products of Binary Matroids}},
author = {Houshan Fu and Yujiao Ma and Suijie Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29227},
eprint = {2609.29227},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29227},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Represented Tensor Products of Binary Matroids
AU - Houshan Fu
AU - Yujiao Ma
AU - Suijie Wang
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29227
UR - https://arxiv.org/abs/2609.29227
AB - For binary matroids M,N representable over a common field F, the Kronecker product of their F-representations defines a matroid T_F(M,N) independent of the chosen representations. We classify when this represented tensor product is regular, cographic, graphic, or binary. For simple nonfree factors, regularity holds exactly when, up to interchange, one factor is a cactus matroid and the other is outerplanar, or one is a triangular cactus matroid and the other is series--parallel. Cographicity holds exactly in the first case. For simple factors with nonempty ground sets, graphicity holds exactly when one factor is free and the other is graphic. For fixed factors, regularity, cographicity, and graphicity are independent of the common representation field, although the isomorphism type may vary with its characteristic. Products of at least three simple nonfree factors are nonregular.
ER -