Embracing exchange sequences and oriented matroid polyhedron diameter

@misc{berczi2026embracing,
  title = {{Embracing exchange sequences and oriented matroid polyhedron diameter}},
  author = {Kristóf Bérczi and Kolja Knauer and Luis Pedro Montejano and Benedek Nádor},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.19573},
  eprint = {2606.19573},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.19573},
}

TY  - UNPB
TI  - Embracing exchange sequences and oriented matroid polyhedron diameter
AU  - Kristóf Bérczi
AU  - Kolja Knauer
AU  - Luis Pedro Montejano
AU  - Benedek Nádor
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2606.19573
UR  - https://arxiv.org/abs/2606.19573
AB  - We reduce the embracing exchange distance of bases of oriented matroids to the metric of oriented matroid polyhedra. This allows us to disprove recent conjectures of Caoduro, Khodamoradi, Paat, and Shepherd and of Bérczi and Nádor. On the other hand, we show that any two embracing bases of an oriented matroid of rank r can be transformed into each other in at most 2r^log_2(r)+3 steps and in at most r steps in a graphic oriented matroid or a Lawrence oriented matroid, thus confirming the conjecture in these cases.
ER  -