The algebra of balanced dessins

Abstract

This paper gives a key definition, for a new approach to dessins and algebraic numbers. The distant goal is to construct from each dessin $D$ an algebraic number ${\eta }_D$, in a systematic and useful way. The algebra of balanced dessins is generated by formal sums ${\psi }_D$ of dessins, intended to be intermediate between $D$ and ${\eta }_D$.

2 pages