Plane trees and Shabat polynomials
type: Item
instance of: scholarly article
title: Plane trees and Shabat polynomials
zbMATH Open document ID: 0851.05098
DOI: 10.1016/0012-365X(95)00127-I
author: Jean Bétréma
author: Alexander K. Zvonkin
published in: Discrete Mathematics
publication date: 1996-11-24T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 05E25
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 897595
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: plane trees
zbMATH Keywords: Shabat polynomials
zbMATH Keywords: complex polynomials
zbMATH Keywords: Galois group actions
zbMATH Keywords: irreducible polynomial
MaRDI profile type: Publication
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full work available at URL: 0012-365x(95)00127-i
OpenAlex ID: W2078374688
description: scientific article; zbMATH DE number 897595