Title: Davenport-Zannier Polynomials and Dessins D'Enfants
Description: The French expression "dessins d'enfants" means children's drawings. This term was coined by the great French mathematician Alexandre Grothendieck in order to denominate a method of pictorial representation of some highly interesting classes of polynomials and rational functions. The polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics.
Subjects: Mathematics, Dessins d'enfants (Mathematics), Arithmetical algebraic geometry, Trees (Graph theory), Galois theory, Polynomials, Algebraic fields, Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Dessins d'enfants, Belyĭ theory, Combinatorics -- Graph theory -- Trees, Combinatorics -- Graph theory -- Planar graphs; geometric and topological aspect, Combinatorics -- Graph theory -- Signed and weighted graphs, Combinatorics -- Algebraic combinatorics -- Group actions on combinatorial structures, Number theory -- Algebraic number theory: global fields -- Galois theory, Field theory and polynomials -- General field theory -- Special polynomials, Field theory and polynomials -- Computational aspects of field theory and polynomials -- Computational aspects of field theory and polynomials, Group theory and generalizations -- Permutation groups -- Primitive groups, Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Dessins d'enfants, Belyi  theory