Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a dessin d'enfant (French for a "child's drawing", plural dessins d'enfants, "childrens' drawings") is a type of graph drawing used to study Riemann surfaces and to provide combinatorial invariants for the action of the absolute Galois group of the rational numbers. Intuitively, a dessin d'enfant is simply a graph, with its vertices colored black and white, embedded onto an oriented surface which in many cases is simply a plane. In order for the coloring to exist, the graph must be bipartite. The surface and the embedding may be described combinatorially using a rotation system, a cyclic order of the edges surrounding each vertex of the graph that describes the order in which the edges would be crossed by a path that travels clockwise on the surface in a small loop around the vertex. Any dessin can be used to provide the surface on which it is embedded with a structure as a Riemann surface, and any Riemann surface can be described in this way. The absolute Galois group transforms Riemann surfaces into each other, and thereby also transforms the underlying dessins.

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