TL;DR
This paper reinterprets and generalizes the operation of joining coset diagrams as a connected sum on dessins d'enfants, providing new insights and examples in the study of algebraic and geometric structures.
Contribution
It introduces a novel generalization of the joining operation for coset diagrams as a connected sum on dessins d'enfants, expanding the theoretical framework.
Findings
Reinterpretation of coset diagram joining as connected sum
Generalization of the operation to dessins d'enfants
Presentation of multiple illustrative examples
Abstract
An operation of joining coset diagrams for a given group, introduced by Higman and developed by Conder in connection with Hurwitz groups, is reinterpreted and generalised as a connected sum operation on dessins d'enfants of a given type. A number of examples are given.
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