Year: 2024
Type: preprint
Abstract: We show that, given a rank 3 affine root system $Φ$ with Weyl group $W$, there is a unique oriented matroid structure on $Φ$ which is $W$-equivariant and restricts to the usual matroid structure on rank 2 subsystems. Such oriented matroids were called oriented matroid root systems in Dyer-Wang (2021), and are known to be non-unique in higher rank. We also show uniqueness for any finite root system or "clean" rank 3 root system (which conjecturally includes all rank 3 root systems).
Source: arXiv (Cornell University)
Authors: Barkley, Grant, Tung, Katherine
Institution: Harvard University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4403575122