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Bipartite graphs occur in many parts of mathematics, and their embeddings into orientable compact surfaces are an old subject. A new interest comes from the fact that these embeddings give dessins d’enfants providing the surface with a unique structure as a Riemann surface and algebraic curve. In this paper, we study the (surprisingly many different)… (More)

A compact Riemann surface of genus g > 1 has different uniform dessins d’enfants of the same type if and only if its surface group S is contained in different conjugate Fuchsian triangle groups ∆ and α∆α. Tools and results in the study of these conjugates depend on whether ∆ is an arithmetic triangle group or not. In the case when ∆ is not arithmetic the… (More)

Dessins d’enfants can be seen as bipartite graphs embedded in compact orientable surfaces. According to Grothendieck and others, a dessin uniquely determines a complex structure on the surface, even an algebraic structure as a projective algebraic curve defined over a number field. Combinatorial properties of the dessin should therefore determine the… (More)

- Gareth A. Jones, J. Mary Jones, Jürgen Wolfart
- J. Comb. Theory, Ser. B
- 2008

- Cori Hypermaps, Dessins d’Enfants, David Singerman, Jürgen Wolfart
- 2008

This paper explains some facts probably known to experts and implicitely contained in the literature about dessins d’enfants but which seem to be nowhere explicitely stated. The 1skeleton of every regular Cori hypermap is the Cayley graph of its automorphism group, embedded in the underlying orientable surface. Conversely, every Cayley graph of a finite… (More)

The subject of this article belongs to the general question Under which condition(s) suitably normalized transcendental functions take algebraic values at algebraic arguments? Already the classical examples of Weierstrass’ result concerning the exponential function and Theodor Schneider’s result about the elliptic modular function show that arguments and… (More)

Dessins d’enfants can be regarded as bipartite graphs embedded in compact orientable surfaces. According to Grothendieck and others, a dessin uniquely determines a complex structure on the surface, and even an algebraic structure (as a projective algebraic curve defined over a number field). The general problem of how to determine all properties of the… (More)

- Raymond Brummelhuis, Norbert Röhrl, +7 authors Oleg H. Izhboldin
- 2002

We show that the modulus of the Coulomb Dirac oper-<lb>ator with a sufficiently small coupling constant bounds the modulus<lb>of the free Dirac operator from above up to a multiplicative constant<lb>depending on the product of the nuclear charge and the electronic<lb>charge. This bound sharpens a result of Bach et al [2] and allows<lb>to prove the… (More)

- Anna Elisabeth Posingies, Christoph Markschies, Peter Frensch, Jürg Kramer, Ulf Kühn, Jürgen Wolfart
- 2010

In this dissertation non-holomorphic Eisenstein series and Dessins d’Enfants are considered. Non holomorphic Eisenstein series are created out of subgroups of the modular group by summing up over all elements modulo the stabilizer of a cusp. The second main object, Dessins d’Enfants, are bipartite graphs that are embedded into topological surfaces. There is… (More)

- Ernesto Girondo, David Torres–Teigell, Jürgen Wolfart
- 2014

In previous work the authors introduced certain Shimura curves that possess different uniform dessins d’enfants (equivalently, uniform Belyi functions). They are all quasiplatonic and therefore they can be defined over its field of moduli. In this paper the authors determine fields of moduli and some fields of definition of these curves and their related… (More)