2022/06/14 by Vincent Umutabazi, Umutabazi, Vincent
Mathematics · #05E99 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2206.06538
openalex publication_date 2022/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove that if the dual of a Bruhat interval in a Weyl group is a zircon, then that interval is rationally smooth. Investigating when the converse holds, and drawing inspiration from conjectures by Delanoy, leads us to pose two conjectures. If true, they imply that for Bruhat intervals in type A, duals of smooth intervals, zircons, and being isomorphic to lower intervals are all equivalent. As a verification, we have checked our conjectures in types An, n≤ 8.