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PreprintarXiv licencearXiv

The Boolean lattice ℬ6 is not a sphere order

  • David A. Meyer
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Abstract

Using the equivalence of sphere order representations of posets with Minkowski space embeddings, we show that the Boolean lattice ℬ6 is not a sphere order. This is the first explicit finite example of a poset that is not a sphere order.

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Cite

BibTeXRIS
BibTeX
@misc{meyer2026boolean,
  title = {{The Boolean lattice $\mathcalB_6$ is not a sphere order}},
  author = {David A. Meyer},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02329},
  eprint = {2610.02329},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02329},
}
RIS
TY  - UNPB
TI  - The Boolean lattice ℬ_6 is not a sphere order
AU  - David A. Meyer
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02329
UR  - https://arxiv.org/abs/2610.02329
AB  - Using the equivalence of sphere order representations of posets with Minkowski space embeddings, we show that the Boolean lattice ℬ_6 is not a sphere order. This is the first explicit finite example of a poset that is not a sphere order.
ER  -