Strong $\mathfrak{sl}_2$ Actions and Symmetric Chain Decompositions

Nate Harman; Rylan Rosas; Charles Troutman III; Chris Wu

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arXiv · 2610.24148

Strong $\mathfrak{sl}_2$ 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 $\mathfrak{sl}_2$-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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BibTeX RIS

Nate Harman, Rylan Rosas, Charles Troutman III, Chris Wu. 2026-10-16. Strong $\mathfrak{sl}_2$ Actions and Symmetric Chain Decompositions. https://arxiv.org/abs/2610.24148

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