Transitivity And Connectivity Of Permutations
Ossona De Mendez, Patrice ; Rosenstiehl, Pierre
HAL, hal-00005618 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-05
Classification:  connected permutation,  hypermap,  05A19 - 05C30,  [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] 
@article{hal-00005618,
     author = {Ossona De Mendez, Patrice and Rosenstiehl, Pierre},
     title = {Transitivity And Connectivity Of Permutations},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00005618}
}

Ossona De Mendez, Patrice; Rosenstiehl, Pierre. Transitivity And Connectivity Of Permutations. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00005618/