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PreprintarXiv licencearXiv

Shellability of semidistributive lattices

  • Shuo Chen
  • Adrien Segovia
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Abstract

We prove that join-semidistributive shellable lattices are join-extremal. In particular, every semidistributive shellable lattice is extremal. Together with known results, this gives the equivalence between extremality, left modularity, EL-shellability and shellability for semidistributive lattices. This answers open questions of Mühle and Segovia.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026shellability,
  title = {{Shellability of semidistributive lattices}},
  author = {Shuo Chen and Adrien Segovia},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07382},
  eprint = {2609.07382},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07382},
}
RIS
TY  - UNPB
TI  - Shellability of semidistributive lattices
AU  - Shuo Chen
AU  - Adrien Segovia
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07382
UR  - https://arxiv.org/abs/2609.07382
AB  - We prove that join-semidistributive shellable lattices are join-extremal. In particular, every semidistributive shellable lattice is extremal. Together with known results, this gives the equivalence between extremality, left modularity, EL-shellability and shellability for semidistributive lattices. This answers open questions of Mühle and Segovia.
ER  -