Graphs, stable permutations, and Cuntz algebra automorphisms

Stable permutations are a class of permutations that arises
in the study of the automorphism group of the Cuntz algebra.
In this talk I will define stable permutations, explain the
connection to the automorphisms of the Cuntz algebra, and
describe the main results known about them. I will then
present a characterization of stable permutations in terms
of certain associated graphs. As a consequence of this
characterization I will prove a conjecture in [Advances in Math.,
381(2021) 107590], and I will characterize explicitly stable
4 and 5-cycles.

This is joint work with Roberto Conti and Gleb Nenashev.