Transitivity And Connectivity Of Permutations
Résumé
It was observed for years, in particular in quantum physics, that the number of connected permutations of [0; n] (also called indecomposable permutations), i. e. those f such that for any i < n there exists j > i with f(j) < i, equals the number of pointed hypermaps of size n, i. e. the number of transitive pairs of permutations of a set of cardinality n with a distinguished element. The paper establishes a natural bijection between the two families. An encoding of maps follows.