Séminaire Lotharingien de Combinatoire, B13h (1986), 12 p.
[Formerly: Publ. I.R.M.A. Strasbourg, 1986, 316/S-13, p. 45-57.]
Gareth Jones
Operations on Maps and Hypermaps
Abstract.
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 following version is available:
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.