Primitive Groups are rare (but useful)
 
 
Description:  A hypermap is, in its topological form, a cellular embedding of a connected hypergraph. Hypermaps can be modified by some operations, like duality (the operation that interchanges hypervertices and hyperfaces on oriented hypermaps). The notion of duality index was created to measure how far a hypermap is from being self-dual, and that notion plays an important role in this talk.
We say that an oriented regular hypermap has duality-type $\{l,n\}$ if $l$ is the valency of its vertices and $n$ is the valency of its faces. We will present some properties of the duality index of oriented regular hypermaps and we will prove that for each pair $n, l \in \mathbb{N}$, with $n,l ≥ 2$ (but not both equal to 2), it is possible to find an oriented regular hypermap with extreme duality index (very distant from being self-dual) and of duality-type $\{l,n\}$, even if we are restricted to hypermaps with alternating or symmetric monodromy group. This goal is achieved by using some properties of primitive groups, since (for large order) most of them are alternating or symmetric groups.
Date:  2012-10-17
Start Time:   14:00
Speaker:  Daniel Pinto (CMUC, Univ. Coimbra)
Institution:  Centre for Mathematics of the University of Coimbra
Place:  Sala 5.5
Research Groups: -Geometry
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