Publication details
Calculating entries of unitary 𝑆𝐿𝟹-friezes
- authored by
- Lucas Surmann
- Abstract
In this article we consider tame $ SL_3 $-friezes that arise by specializing a cluster of Pl\"ucker variables in the coordinate ring of the Grassmannian $ \mathscr{G}(3,n) $ to $ 1 $. We show how to calculate arbitrary entries of such friezes from the cluster in question. Let $ \mathscr{F} $ be such a cluster. We study the set $ \mathscr{F}_x $ of cluster variables in $ \mathscr{F} $ that share a given index $ x $ and derive a structure Theorem for $ \mathscr{F}_x $. These sets prove central to calculating the first and last non-trivial rows of the frieze. After that, simple recursive formulas can be used to calculate all remaining entries.
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- Type
- Article
- Journal
- Journal of Combinatorial Algebra
- ISSN
- 2415-6302
- Publication date
- 11.03.2025
- Publication status
- E-pub ahead of print
- Peer reviewed
- Yes
- Research Area (based on ÖFOS 2012)
- Combinatorics, Algebra, Graph theory
- Electronic version(s)
-
https://doi.org/10.4171/JCA/111 (Access:
Open)
https://doi.org/10.48550/arXiv.2404.09811 (Access: Open)