Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7223060181