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PreprintCC BY 4.0arXiv

Strong sl2 Actions and Symmetric Chain Decompositions

  • Nate Harman
  • Rylan Rosas
  • Charles Troutman III
  • Chris Wu
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Abstract

We introduce a notion of a strong sl2-action on a poset, and conjecture the existence of such an action is equivalent to the existence of a symmetric chain decomposition of that poset. We explain the intuition behind the conjecture, go through a number of explicit examples, and prove some special cases and relaxations of the conjecture. Then we explain a computational experiment where we tested the conjecture on millions of randomly constructed rank-symmetric, rank-unimodal, and strongly Sperner posets.

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Cite

BibTeXRIS
BibTeX
@misc{harman2026strong,
  title = {{Strong $\mathfraksl_2$ Actions and Symmetric Chain Decompositions}},
  author = {Nate Harman and Rylan Rosas and Charles Troutman III and Chris Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24148},
  eprint = {2610.24148},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24148},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Strong sl_2 Actions and Symmetric Chain Decompositions
AU  - Nate Harman
AU  - Rylan Rosas
AU  - Charles Troutman III
AU  - Chris Wu
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.24148
UR  - https://arxiv.org/abs/2610.24148
AB  - We introduce a notion of a strong sl_2-action on a poset, and conjecture the existence of such an action is equivalent to the existence of a symmetric chain decomposition of that poset. We explain the intuition behind the conjecture, go through a number of explicit examples, and prove some special cases and relaxations of the conjecture. Then we explain a computational experiment where we tested the conjecture on millions of randomly constructed rank-symmetric, rank-unimodal, and strongly Sperner posets.
ER  -