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Maximal matroids and counterexamples
Abstract
Jackson and Tanigawa conjectured that the rigidity matroid ℛdn and the hyperconnectivity matroid ℋdn are the unique maximal matroids in the posets of {Kd+2, Kd+2,d+2}-matroids and {Kd+2,Kd+1,d+1}-matroids, respectively. We disprove these conjectures by showing the existence of maximal matroids that are distinct from the proposed candidates.
Related
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BibTeX
@misc{bulavka2026maximal,
title = {{Maximal matroids and counterexamples}},
author = {Denys Bulavka and Martin Tancer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.14663},
eprint = {2606.14663},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.14663},
}
RIS
TY - UNPB
TI - Maximal matroids and counterexamples
AU - Denys Bulavka
AU - Martin Tancer
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2606.14663
UR - https://arxiv.org/abs/2606.14663
AB - Jackson and Tanigawa conjectured that the rigidity matroid ℛ^d_n and the hyperconnectivity matroid ℋ^d_n are the unique maximal matroids in the posets of {K_d+2, K_d+2,d+2}-matroids and {K_d+2,K_d+1,d+1}-matroids, respectively. We disprove these conjectures by showing the existence of maximal matroids that are distinct from the proposed candidates.
ER -