Colored triangulations of arbitrary dimensions are stuffed Walsh maps

Understand

Regular edge-colored graphs encode colored triangulations of pseudo-manifolds.

• Here we study families of edge-colored graphs built from a finite but arbitrary set of building blocks, which extend the notion of $p$-angulations to arbitrary dimensions.
• We prove the existence of a bijection between any such family and some colored combinatorial maps which we call stuffed Walsh maps.
• Those maps generalize Walsh's representation of hypermaps as bipartite maps, by replacing the vertices which correspond to hyperedges with non-properly-edge-colored maps.