Dear Gap Forum:

Mr. Aslam wrote:

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Dear Gap Forum,

I am looking for an algorithm(s) that would enumerate
a permutation group (from a set of genrators) such
that each element of the
group is represented as a product of the disjoint permutations
(which would be from the set of the generators).

That is if each element pi of the group G is represented as
pi = g1*g2* ... gr ,
(where r is clearly a polynomial in the degree of the group),

then g1,g2, .. gr are mutually disjoint.

Here the size of set of generators could be a polynomial in r.
Clearly, it is not important whether the generators are strong are not.

Hope to receive some references in this direction.

See
Gray Codes for Reflection Groups, J. H. Conway, N. J. A. Sloane and A. R. Wilks,

Graphs and Combinatorics,
5 (1989), pp. 315-325.
available at
http://www.research.att.com/~njas/doc/gp.html

Thanking you all.
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--
David Joyner, Assoc Prof of Math
US Naval Academy, Annapolis, MD 21402
(410)293-6738
wdj@nadn.navy.mil
http://web.usna.navy.mil/~wdj/homepage.html
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"A Mathematician is a machine for turning
coffee into theorems." Alfred Renyi