Dessins d’enfants: From polynomials through Belyĭ functions to weighted trees

2020 ◽  
pp. 9-18
Keyword(s):  
Weighted Trees ◽  
Dessins D’Enfants ◽  
Belyi Functions ◽  
Dessins D'enfants

scholarly journals Davenport–Zannier polynomials over ℚ

2018 ◽  
Vol 14 (04) ◽  
pp. 925-974
Author(s):  
Fedor Pakovich ◽  
Alexander K. Zvonkin
Keyword(s):  
Galois Theory ◽  
Minimum Degree ◽  
Additional Material ◽  
Black And White ◽  
Weighted Trees ◽  
Dessins D’Enfants ◽  
Plane Trees ◽  
The Difference ◽  
Dessins D'enfants ◽  
Weighted Plane

In this paper, we study pairs of polynomials with a given factorization pattern and such that the degree of their difference attains its minimum. We call such pairs of polynomials Davenport–Zannier pairs (DZ-pairs). The paper is devoted to the study of DZ-pairs with rational coefficients. In our earlier paper [F. Pakovich and A. K. Zvonkin, Minimum degree of the difference of two polynomials over [Formula: see text], and weighted plane trees, Selecta Math., (N.S.) 20(4) (2014) 1003–1065], in the framework of the theory of dessins d’enfants, we established a correspondence between DZ-pairs and weighted bicolored plane trees. These are bicolored plane trees whose edges are endowed with positive integral weights. When such a tree is uniquely determined by the set of black and white degrees of its vertices, it is called unitree, and the corresponding DZ-pair is defined over [Formula: see text]. In our cited paper above, we classified all unitrees. In this paper, we compute all the corresponding polynomials. We also present some additional material concerning the Galois theory of DZ-pairs and weighted trees.

Dessins d'enfants kurumba de Mengao, Haute-Volta

1981 ◽  
Vol 51 (1) ◽  
pp. 251-264 ◽  
Author(s):  
Annemarie Schweeger-Hefel
Keyword(s):  
Dessins D’Enfants ◽  
Dessins D'enfants

Davenport–Zannier Polynomials and Dessins d’Enfants

2020 ◽  
Author(s):  
Nikolai Adrianov ◽  
Fedor Pakovich ◽  
Alexander Zvonkin
Keyword(s):  
Dessins D’Enfants ◽  
Dessins D'enfants

La reconstruction des enveloppes psychiques et environnementales dans les dessins d’enfants des rues en Haïti : une étude post-séisme

2017 ◽  
Vol 82 (1) ◽  
pp. 89-103 ◽  
Author(s):  
Amira Karray ◽  
Daniel Derivois ◽  
Lisbeth Brolles ◽  
Iris Wexler Buzaglo
Keyword(s):  
Dessins D’Enfants ◽  
Dessins D'enfants
Sign in / Sign up

Export Citation Format

Share Document