# Degree-d-invariant laminations

## TL;DR

This paper explores degree-d-invariant laminations as models for polynomial dynamics, introduces primitive majors as a parameterization tool, and presents a combinatorial method for computing core entropy without Hubbard trees.

## Contribution

It introduces primitive majors as a new combinatorial framework and provides a direct method to compute core entropy for degree-d polynomials.

## Key findings

- Primitive majors form a spine for polynomial parameter spaces.
- A combinatorial approach allows core entropy calculation without Hubbard trees.
- The framework models polynomial dynamics via invariant laminations.

## Abstract

Degree-$d$-invariant laminations of the disk model the dynamical action of a degree-$d$ polynomial; such a lamination defines an equivalence relation on $S^1$ that corresponds to dynamical rays of an associated polynomial landing at the same multi-accessible points in the Julia set. Primitive majors are certain subsets of degree-$d$-invariant laminations consisting of critical leaves and gaps. The space $\textrm{PM}(d)$ of primitive degree-$d$ majors is a spine for the set of monic degree-$d$ polynomials with distinct roots and serves as a parameterization of a subset of the boundary of the connectedness locus for degree-$d$ polynomials. The core entropy of a postcritically finite polynomial is the topological entropy of the action of the polynomial on the associated Hubbard tree. Core entropy may be computed directly, bypassing the Hubbard tree, using a combinatorial analogue of the Hubbard tree within the context of degree-$d$-invariant laminations.