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## Re: uniq matrix odering

 From: Daniel Heiserer Subject: Re: uniq matrix odering Date: Thu, 30 Sep 1999 16:12:59 +0200

```Hi,

>
> This seems to be a problem from the combinatorial analysis,

Yep.

> which I dunno.  Still I'd like to clarify: are you going to
> permute rows and columns as a hole, i.e., change the places
> of say, the i-th and the j-th rows/columns, or you can

Yep.

> permute the elements within a row/column?  In the latter case
> it seems that you can reach _any_ configuration that has
> the predefined number of 1s (i.e., the same number of 1s,

You are right. My rule is: for ONE step you are allowed to permute
either a column OR a row.

> In this case there will also appear a problem
> to find the way of doing this in a minimum number of steps.

yep. This would be step number two.
Step one is to find a criteria or configuration which is unique.
Of course it is important to reach this configuration from
any pre-configuration as fast as possible.

>
> On Thu, 30 Sep 1999, Daniel Heiserer wrote:
>
> > I allow infinite permutations (exchanges of rows):
> > a_ij ==> a_kj && a_kj ==> a_ij  for all j's (using an intermediate
> > storage of course)
> >
> > octave>> a=a([perturb(1:size(a,1))],:);
> > where "perturb" should be function which just reorders the elements of a
> > vector (no matter how).
> > I also allow infinite permutaions of columns:
> > a_ij ==> a_ik && a_ik ==> a_ij  ""
> > octave>> a=a(:,[perturb(1:size(a,2))]);
> >
> > If I see it right the number of allowable permutations is m!*n! for a m
> > by n Matrix.
> >
> > What I would like to know is if there is one configuration *defineabele*
> > which I could alwasy reach, regardless with which permutation I start.
> > The key question is how this end-configuration could be defined, what is
> > the criteria. Can I define a criteria which gives me for a certain norm
> > a sort of optimization problem, with a unique endsolution (assuming
> > there is no symmetry).
> >
> > In fact this comes from a topological problem. And I try to find a sort
> > of
> > a norm for 3D-topologies.

--
Mit freundlichen Gruessen
Daniel Heiserer
-----
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Dipl.-Phys. Daniel Heiserer, BMW AG, Knorrstrasse 147, 80788 Muenchen
Abteilung EK-20
Tel.: 089-382-21187, Fax.: 089-382-42820

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