Dessins, their deltamatroids and partial duals
Abstract
Given a map $\mathcal M$ on a connected and closed orientable surface, the deltamatroid of $\mathcal M$ is a combinatorial object associated to $\mathcal M$ which captures some topological information of the embedding. We explore how deltamatroids associated to dessins d'enfants behave under the action of the absolute Galois group. Twists of deltamatroids are considered as well; they correspond to the recently introduced operation of partial duality of maps. Furthermore, we prove that every map has a partial dual defined over its field of moduli. A relationship between dessins, partial duals and tropical curves arising from the cartography groups of dessins is observed as well.
 Publication:

arXiv eprints
 Pub Date:
 June 2015
 arXiv:
 arXiv:1506.02441
 Bibcode:
 2015arXiv150602441M
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 34 pages, 20 figures. Accepted for publication in the SIGMAP14 Conference Proceedings