Transitivity And Connectivity Of Permutations

Patrice Ossona de Mendez (1) , Pierre Rosenstiehl (1)

1 CAMS - Centre d'Analyse et de Mathématique sociales

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.

Mots clés: connected permutation; hypermap

Domaines: Combinatoire [math.CO]

Patrice Ossona de Mendez, Pierre Rosenstiehl. Transitivity And Connectivity Of Permutations. Combinatorica, 2004, 24(3), pp.487 - 501. ⟨10.1007/s00493-004-0029-4⟩. ⟨hal-00005618⟩