Map operations and k-orbit maps

A k-orbit map is a map with k flag-orbits under the action of its automorphism group. We give a basic theory of k-orbit maps and classify them up to k 4. “Hurwitz-like” upper bounds for the cardinality of the automorphism groups of 2orbit and 3-orbit maps on surfaces are given. Furthermore, we consider effects of operations like medial and truncation on k-orbit maps and use them in classifying 2-orbit and 3-orbit maps on surfaces of small genus. MSC (2000): Primary: 51M20; Secondary: 05C10, 05C30, 52B70. Key words: maps, monodromy groups, medials of maps, truncations of maps, polyhedra, k-orbit maps.

• Type: Journal
• Year: 2010
• Where: JCT
• Authors: Alen Orbanic, Daniel Pellicer, Asia Ivic Weiss
• Keywords: 3-orbit Maps, Automorphism Groups, JCT 2010, K-orbit Maps