Unstable maps

A map which is non-orientable or has non-empty boundary has a canonical double cover which is orientable and has empty boundary. The map is called stable if every automorphism of this cover is a lift of an automorphism of the map. This note describes several infinite families of unstable maps, and relates them to similar phenomena for graphs, hypermaps and Klein surfaces.Comment: 11 pages, 4 figure

Exotic behaviour of infinite hypermaps

This is a survey of infinite hypermaps, and of how they can be constructed by using examples and techniques from combinatorial group theory, with particular emphasis on phenomena which have no analogues for finite hypermaps.<br/

Integrating social media with existing knowledge and information for crisis response

Existing studies on social media in the context of crisis have studied the content of items and their patterns of transmission. However, social media content generated during a crisis will generally be unstructured and only reflect the immediate experiences of the authors, while the volumes of data created can make rapid interpretation very challenging. Crisis situations can be characterized with various expected attributes. In many situations there will be large amounts of information relevant to the situation already available. We argue that existing natural language engineering technologies can be integrated with emerging social media content utilization techniques for more powerful exploitation of social media content in crisis response

Regular dessins with a given automorphism group

Dessins d'enfants are combinatorial structures on compact Riemann surfaces defined over algebraic number fields, and regular dessins are the most symmetric of them. If G is a finite group, there are only finitely many regular dessins with automorphism group G. It is shown how to enumerate them, how to represent them all as quotients of a single regular dessin U(G), and how certain hypermap operations act on them. For example, if G is a cyclic group of order n then U(G) is a map on the Fermat curve of degree n and genus (n-1)(n-2)/2. On the other hand, if G=A_5 then U(G) has genus 274218830047232000000000000000001. For other non-abelian finite simple groups, the genus is much larger.Comment: 19 page

Primitive permutation groups containing a cycle

The primitive finite permutation groups containing a cycle are classified. Of these, only the alternating and symmetric groups contain a cycle fixing at least three points. The contributions of Jordan and Marggraff to this topic are briefly discussed.Comment: 6 page