Newsgroups: sci.math
From: haoyuep@aol.com (Dan Hoey)
Date: 31 Oct 2000 12:51:31 GMT
Subject: Re: The mathematics of dealing cards

"Gary Davis" <davis@unbsj.ca> writes:
>Ah yes, three responses, so far, for which I thank you all.  But they all
>deal with SHUFFLING.  My problem requires NOT SHUFFLING.

The response by Steve Lord was to study permutations.  That is correct
and pertinent to your problem.  Permutations are rearrangements in the
order of a set, and are applicable to deterministic rearrangements such
as dealing and sorting, as well as to random rearrangements such as
shuffling.

You would also benefit by investigating the theory of finite groups,
which applies to combining permutations by composition, and inversely to
analyzing permutations as compositions of other permutations.  You
may also seek information on the "symmetric group" S_n, which is the
group of all permutations on n objects.  In a sense these three terms
apply to different ways of looking at the same topic, so you will be
in the right area no matter which term you read about.

You should be able to find information on these topics in any introductory
abstract algebra text at the undergraduate level.  Be careful not to
dismiss discussions of topics that do not seem to apply to your problem,
as you did with "shuffling".  The applications of group theory arise
by surprising pathways.

Dan Hoey
haoyuep@aol.com