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Neither simpliciality nor mutation connectivity: conjectures of Las Vergnas and Cordovil-Las Vergnas fail
Abstract
We construct a simple rank-$7$ oriented matroid on $24$ elements with no simplicial tope, disproving the Las Vergnas simplex conjecture from 1980. We then show that the mutation graph on uniform oriented matroids is disconnected for infinitely many values of rank r and ground-set size n, disproving the Cordovil--Las Vergnas conjecture from 1988.
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BibTeX
@misc{gu2026neither,
title = {{Neither simpliciality nor mutation connectivity: conjectures of Las Vergnas and Cordovil-Las Vergnas fail}},
author = {Qiyuan Gu and Kolja Knauer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15850},
eprint = {2609.15850},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15850},
}
RIS
TY - UNPB
TI - Neither simpliciality nor mutation connectivity: conjectures of Las Vergnas and Cordovil-Las Vergnas fail
AU - Qiyuan Gu
AU - Kolja Knauer
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15850
UR - https://arxiv.org/abs/2609.15850
AB - We construct a simple rank-$7$ oriented matroid on $24$ elements with no simplicial tope, disproving the Las Vergnas simplex conjecture from 1980. We then show that the mutation graph on uniform oriented matroids is disconnected for infinitely many values of rank r and ground-set size n, disproving the Cordovil--Las Vergnas conjecture from 1988.
ER -