2020/08/21 by Zhan Jiang, Jiang, Zhan, Michael E. Zieve +1
Mathematics · #20M05 (Secondary) #37F10 (Primary) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Limits and Structures in Graph Theory #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2008.09554
openalex publication_date 2020/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We determine all F,G in C[X] of degree at least 2 for which the semigroup generated by F and G under composition is not the free semigroup on the letters F and G. We also solve the same problem for F,G in X2 C[[X]], and prove partial analogues over arbitrary fields.