2024/08/02 by Hilton, Forrest M.
#37F20 (Primary) 05A19 (Secondary) #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2408.01353
We developed several combinatorial notions about laminations some with clear implications for parameter space. We introduce a simplified class of laminations called finite dynamical laminations (FDL). In order to count FDL, we introduce sibling portraits, of which we provide a comprehensive counting theorem. We provide a characterization of which periodic polygons appear in invariant laminations. We introduce the pullback tree. The base of the pullback tree is a set of laminations, and we show that those laminations are proper and invariant and have a restriction on its critical leaves, so all laminations in the base of the pullback tree correspond to a polynomial. We define the generational FDL graph, and it provides a summary of the combinatorial information we provide about polynomial parameter space.