Plane trees, cartographical groups, and Chebyshev polynomials
type: Item
instance of: scholarly article
title: Plane trees, cartographical groups, and Chebyshev polynomials
zbMATH Open document ID: 0913.14006
DOI: 10.1007/BF02365316
author: Yu. Yu. Kochetkov
published in: Journal of Mathematical Sciences (New York)
publication date: 1998-10-22T00:00:00Z
review text: In this paper, plane trees are studied as a special case of graphs on a Riemann surface (or ``dessins d'enfants'' in Grothendieck's terminology). The first section is devoted to the cartographic group of such a tree \(T\); with a bipartite structure (or ``coloring'') of \(T\), the author associates several subgroups, e.g. the ``monodromy group'' of \(T\). He presents a list of 23 nonelementary irreducible trees and conjectures that it is complete. The section also contains an algorithm to compute the order of the monodromy group. In the second part, the author studies generalized Chebyshev polynomials , i.e. polynomials with at most 2 critical values, and shows that they correspond bijectively to plane trees (via the inverse image of the segment joining the critical values). For several examples, he calculates this polynomial and also the Galois orbits.
Mathematics Subject Classification ID: 14H25
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 33C99
Mathematics Subject Classification ID: 14N10
zbMATH DE Number: 1213207
zbMATH Keywords: dessins d'enfants
zbMATH Keywords: plane trees
zbMATH Keywords: cartographic group
zbMATH Keywords: generalized Chebyshev polynomials
reviewed by: Frank Herrlich
MaRDI profile type: Publication
cites work: Plane trees and classical mathematics
cites work: Cartographical groups and generalized Chebyshev polynomials
cites work: Planar trees and their monodromy groups
cites work: Q3128068
cites work: Q4325462
cites work: Q4364755
cites work: Q3972767
description: scientific article; zbMATH DE number 1213207