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arXiv · 2609.07382

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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Shuo Chen, Adrien Segovia. 2026-09-07. Shellability of semidistributive lattices. https://arxiv.org/abs/2609.07382

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