OpenAlex ·
Strong $\mathfrak{sl}_2$ Actions and Symmetric Chain Decompositions
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2610.24148
- Original
- Read it at the publisher
- Topics
Abstract
We introduce a notion of a strong $\mathfrak{sl}_2$-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.
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