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

Challenges and opportunities of context-aware information access

Ubiquitous computing environments embedding a wide range of pervasive computing technologies provide a challenging and exciting new domain for information access. Individuals working in these environments are increasingly permanently connected to rich information resources. An appealing opportunity of these environments is the potential to deliver useful information to individuals either from their previous information experiences or external sources. This information should enrich their life experiences or make them more effective in their endeavours. Information access in ubiquitous computing environments can be made "context-aware" by exploiting the wide range context data available describing the environment, the searcher and the information itself. Realizing such a vision of reliable, timely and appropriate identification and delivery of information in this way poses numerous challenges. A central theme in achieving context-aware information access is the combination of information retrieval with multiple dimensions of available context data. Potential context data sources, include the user's current task, inputs from environmental and biometric sensors, associated with the user's current context, previous contexts, and document context, which can be exploited using a variety of technologies to create new and exciting possibilities for information access

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

Classification and Galois conjugacy of Hamming maps

We show that for each d>0 the d-dimensional Hamming graph H(d,q) has an orientably regular surface embedding if and only if q is a prime power p^e. If q>2 there are up to isomorphism \phi(q-1)/e such maps, all constructed as Cayley maps for a d-dimensional vector space over the field of order q. We show that for each such pair d, q the corresponding Belyi pairs are conjugate under the action of the absolute Galois group, and we determine their minimal field of definition. We also classify the orientably regular embedding of merged Hamming graphs for q>3