Geodesic
Operations on Maps and Hypermaps
Séminaire lotharingien de combinatoire, Tome 13 (1985)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

The dual map of a cube is an octahedron: they are combinatorially distinct, but they have the same 'size' (e.g. number of edges) and the same automorphism group. Our aim here is to use group theory to construct operations on maps, hypermaps and higher-dimensional structures, which are similar to duality in that they preserve size and symmetry properties. The basic theme is that these combinatorial structures can be represented as transitive permutation representations of appropriate groups, whose outer automorphisms then induce the relevant operations. The ideas outlined here are the result of joint work with David Singerman, John Thornton and Lynne Oames.

The main part of the results of this paper have appeared in the article "On the solutions of a matrix equation," Boll. Un. Mat. Ital. 3-A (1989), 137-145. 
@article{SLC_1985_13_a7,
     author = {Gareth Jones},
     title = {Operations on {Maps} and {Hypermaps}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {13},
     year = {1985},
     url = {http://geodesic.mathdoc.fr/item/SLC_1985_13_a7/}
}
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Gareth Jones. Operations on Maps and Hypermaps. Séminaire lotharingien de combinatoire, Tome 13 (1985). http://geodesic.mathdoc.fr/item/SLC_1985_13_a7/