Duality on hypermaps with symmetric or alternating monodromy group - Pinto, Daniel (Ars mathematica contemporanea, 2012)
Duality is the operation that interchanges hypervertices and hyperfaces on oriented hypermaps. The duality index measures how far a hypermap is from being self-dual. 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. Here, we study some properties of the duality index of oriented regular hypermaps and we prove that for each pair ?$n, l \in \mathbb{N}$?, with ?$n, l \ge 2$? (but not both equal to 2), it is possible to find an oriented regular hypermap with extreme duality index and of duality-type ?$\{l, n\}$?, even if we are restricted to hypermaps with alternating or symmetric monodromy group.
Keywords: alternating group; duality; dualnost; generatorji; generators; graph theory; grupe; primitive group; symmetric group; teorija grafov