Plane trees and Shabat polynomials
The connection between plane trees and Shabat polynomials as a generalization of Chebyshev polynomials is described. Critical points and critical values of complex polynomials, and combinatorial bicolored plane trees are defined. Some geometric forms of corresponding plane trees are shown. Corresponding Shabat polynomials are calculated from a given tree type. Characterizations of the orbits of Galois group actions on trees are discussed. Examples of plane trees and Shabat polynomials are analyzed. A conjecture on the splitting of the discriminant of an irreducible polynomial whose roots generate the field is presented.
scientific article; zbMATH DE number 897595