🚀 go-pugleaf

mnewman@comlab.ox.ac.uk (Matthew Newman) writes:

>Does anyone know the status on the following problem ?

>Let S(n) be the set of all permutations of the integers 1..n
>Let T(n) be the set of all transpositions (i.e. swapping
>two numbers).

>For which n can one find a set B(n) such that for all p in S(n)
>either p is in B(n), or p differs by exactly one transposition
>from an element of B(n), and such that no two elements from B(n)
>differ by exactly one transposition ?

I'd like to append with a more general question:

T(n) forms a generating system for S(n)  (for all n).
How can the combinatorics of this generating system be characterized?
Especially: does there exist a normal form of each generated element from
S(n) over the base T(n) ?

And - excuse please, yet more general - is there a connection to the general
Moebius groups of the Euclidean spaces R_n, where each such Moebius transfor-
mation can be generated by reflections, which are also elements of the
(group-) order 2 ?

Thank you!  
Toni Greil