- Title: Asymptotics in finite monoidal categories
- Authors: Abel Lacabanne, Daniel Tubbenhauer and Pedro Vaz
- Status: To appear in Proc. Amer. Math. Soc. Last update: Thu, 6 Jul 2023 15:09:44 UTC
- ArXiv link: https://arxiv.org/abs/2307.03044
- LaTex Beamer presentation: Slides
We give explicit formulas for the asymptotic growth rate of the number of summands in tensor powers in certain monoidal categories with finitely many indecomposable objects, and related structures.
A few extra words
The main theorems of the note give an explicit formula \(a(n)\) to compute the asymptotic growth of summands
in tensor products \(b(n)\) for a large class of categories.
For example, for dihedral Soergel bimodules one gets: