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
such that for any
i <
n there exists
j >
i with
(
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.
Mathematics Subject Classification (2000):
05A19 - 05C30
To Chantal, that we may stay connected beyond the simple line of time.